Gemara

(Rav Amram): The Halachah follows Rav, who says that Yesh Chupah l'Pesulos. A Mishnah supports this.

(Mishnah): (A Sotah answers) "Amen", that I was not Mezaneh when Mekudeshes, Nesu'ah, Shomeres Yavam (when awaiting Yibum), or after Yibum.

Question: What is the case of Mekudeshes?

She cannot be an Arusah even now, for an Arusah does not drink;

If he warned her and she was secluded during Eirusin, and she drinks after Nisu'in, the water would not test her (for Nisu'in was forbidden after seclusion)! "The man will be clean from sin" - the water tests her only if he is clean from sin!

Answer: Rather, he warned her and she was secluded during Eirusin, and he had Chupah without Bi'ah. This teaches that Chupah takes effect on Pesulos.

Objection (Rava): The Mishnah cannot be correct!

(Beraisa): "Other than your husband" - the water tests her only if her husband had Bi'ah with her before the adulterer.

Answer (Rami bar Chama): Her husband had Bi'ah with her during Kidushin.

Objection: The corresponding case of a Shomeres Yavam is when the Yavam had Bi'ah with her in her father's house (i.e. while awaiting Yibum). If so she is not called Shomeres Yavam. She is a full wife!

This Mishnah was brought to support Rav, who says that Bi'ah (without intent for Yibum) acquires in all respects. He cannot explain why it calls her Shomeres Yavam!

Rishonim

Tosfos (Kidushin 12b DH mi'Shum): Rav lashes one who is Mekadesh through Bi'ah. R. Tam says that this is because it needs witnesses on the Bi'ah or the seclusion, and this is lowly. This is difficult, for one who does Yibum without Ma'amar is lashed due to Rav's law. This is not due to witnesses, for Yibum depends only on Bi'ah! Rather, the Ri says that it is lewd to make an initial acquisition through Bi'ah. Rav similarly lashes for Kidushin without prior arrangement.

Ritva (Kidushin 12b DH d'Rav): The lashes are not for Bi'ah in front of witnesses. It suffices to have witnesses on the seclusion, and this is needed even if he was Mekadesh first! Rather, it is because his first connection to her is Bi'ah. This is like Zenus.

Aruch ha'Shulchan (EH 166:9): The Rambam and Poskim did not need to mention that Yibum requires Edei Yichud. Some Rishonim say so explicitly, e.g. Shiltei ha'Giborim and Tosfos.

Shiltei ha'Giborim (38b 4): If Yibum was done without witnesses of seclusion, she is not totally acquired. He cannot exempt her with a Get without Chalitzah. Just like Kidushin and divorce require witnesses, also Yibum and Chalitzah.

Rebuttal (Yam Shel Shlomo 13:25): Yibum does not require Kidushin. It is a mere Mitzvah, therefore witnesses are not needed.

Mishneh l'Melech (Hilchos Yibum 2:4): I am unsure whether or not Yibum requires witnesses, like Kidushin. Or, perhaps just like a Gezeras ha'Kasuv says that Yibum works even if they were Shogegim or Anusim or she was sleeping, the same applies if they were no witnesses.

Question (Yad ha'Melech 2:3: DH Din and Aruch ha'Shulchan EH 166:10): Why is there any doubt? If Yibum needs witnesses, it is like Kidushin, in which he must summons the witnesses. Yibum acquires even b'Shogeg or b'Mezid (intending for Zenus). Surely, in such cases he did not summons witnesses!

Aruch ha'Shulchan (10,11): In Kidushin she must know about the Edim. Here she need not; she can even be sleeping. Perhaps just like the Torah does not require Edim for her, also for him. We find that divorce is Devar sheb'Ervah, which normally requires two witnesses. The Rashba says that his handwriting suffices like witnesses, since it says "v'Chosav Lah Sefer Kerisos." Anything that affects others requires Edim (CM 241:1). Perhaps since this does not affect others (she is forbidden to everyone else anyway), Edim are not needed. This requires investigation.

Note: Pischei Teshuvah (brought below, DH Hen) gives a partial answer to the question.

Poskim

Shulchan Aruch (EH 166:2): Mid'Oraisa, Yibum does not need Kidushin, just Bi'ah. Chachamim enacted not to have Bi'ah with her before being Mekadesh her in front of witnesses (Ma'amar)... If he had Bi'ah with her without a Ma'amar, he acquired her

Rema: This is only if the Bi'ah was in front of witnesses.

Rebuttal (Gra 9): Tosfos in Kidushin connotes that witnesses are not needed. See Tosfos Yevamos 52a DH d'Mekadesh (there, R. Tam explains like the Ri, i.e. he retracted). The Gemara in Yevamos (58a) supports this; we do not say that he had Bi'ah with her without witnesses.

Pischei Teshuvah (6): Yad ha'Melech (Yibum 1:1) says that witnesses are required for Yibum according to the opinion that Kidushin Tofsin in a Yevamah l'Shuk, for then Yibum affects Kidushin. Since we are unsure whether or not Kidushin Tofsin, we should be stringent to say that perhaps Yibum without witnesses acquires. Yad ha'Melech is unsure if Yibum without witnesses is called 'Kivan she'Lo Banah' (he may not do Yibum afterwards). It would seem that we do not say so, for he intended to build, and according to some he acquired her. However, Shiltei ha'Giborim says that he gives a Get and Chalitzah; it seems that he does not allow Yibum.

Note: In any case Yibum affects Kidushin of the Yavam, e.g. if he is Mekadesh his Yevamah's sister after Yibum it does not take effect!

Question (Tosfos R. Akiva Eiger on Mishnah 6:1): If Yibum requires witnesses, why did the Gemara say that if the Yavam had Bi'ah with her in her father's house she is a full wife? Perhaps they had Bi'ah without witnesses! Even though Beis Din will not let her drink unless they know that the Yavam had Bi'ah with her, we can say that he had Bi'ah with her twice, each time in front of one witness. The Ran (Gitin 35b DH v'Lo) says that such witnesses do not join for Kidushin, since this is like capital testimony.

Answer (R. Akiva Eiger): Perhaps the witnesses do not join to make a Sotah drink, for also this is like capital testimony. It is not clear why the Ran needed to say that Kidushin is like capital cases. He should have said that neither Kidushin was valid, since it was not in front of witnesses!

Question (Pischei Teshuvah 6 DH v'Hinei): Presumably, if Yibum needs witnesses it is like Kidushin, in which the man and woman must see the witnesses. We can say that the Yavam and Yevamah did not see the witnesses, but the witnesses saw them!

Answer (Pischei Teshuvah DH Hen): In Kidushin the man and woman must see the witnesses, for otherwise they do not intend for Kidushin. This does not apply to Yibum, for intent is not required. However, this does not answer for the opinion that the Torah voided such Kidushin even if they intended.

Pischei Teshuvah (DH Emnam): Our Sugya is like Rav, who says that Ein Kidushin Tofsin b'Yevamah l'Shuk, therefore witnesses are not needed. In any case, the Mishnah that says that she swears about Zenus while she was a Shomeres Yavam holds that such Zenus forbids her. The Gemara says that this is like Rav Hamnuna or R. Akiva, both of whom hold that Ein Kidushin Tofsin b'Yevamah l'Shuk.

Note: R. Akiva Eiger does not give his source that Beis Din requires witnesses that the Yavam had Bi'ah with her. (The Beis Meir (Sof DH v'Hinei) says that he is not believed about this, for it enables her to drink and become permitted to him. We find that a Kohen is not believed about his wife who was taken captive.) This is difficult, for Beis Din never knows whether or not the water will work, for perhaps he is not clean of sin! Perhaps we rely on his Chezkas Kashrus.

Question (Sha'ar ha'Melech Yibum 2:4):

Beis Shmu'el (2): The Rema seems to require witnesses only when there was no Ma'amar. However, this cannot be; Ma'amar is only mid'Rabanan! Rather, the Rema teaches that if Yibum was done without witnesses then Ma'amar is required because there is no Kidushin mid'Oraisa. However, the Darchei Moshe connotes otherwise.

Aruch ha'Shulchan (12): The Rema holds that Yibum does not require Edim. However, since it is called 'Kichah' (like Kidushei Kesef), mid'Rabanan we require Edim or publicity. They merely need to witness his intent for Yibum. Therefore, it is possible that the Bi'ah itself was (later) Shogeg or Mezid.

Beis Meir (DH v'Davka): Why is anyone unsure about this? Davar sheb'Ervah always requires two witnesses! It is a Chov to others. Others are now Chayav Misah for Bi'ah with the Yevamah!

Or Some'ach Melachim 2:1 DH b'Firush: According to the Poskim that Yibum must be in front of witnesses, this is why a king does not do Yibum (it is undignified to have Bi'ah in front of witnesses).