Gemara

(Mishnah): Regarding a Safek Bechor, whether human or animal, whether it is a Kosher or Tamei species, ha'Motzi mi'Chavero Alav ha'Re'ayah. (The burden of proof (that it is a Bechor) is on the one who wants to take, i.e. the Kohen, who wants to get five Shekalim, the animal, or a Seh in place of a donkey.)

Bava Metzi'a 6b (Rav Hamnuna): If a Kohen took a Safek Bechor, we do not force him to return it, for ha'Motzi mi'Chavero Alav ha'Re'ayah (perhaps it is truly a Bechor).

Rejection (Rabah): Perhaps we force the Kohen to return it.

Support (R. Chananya - Beraisa): A Safek (perhaps it belongs to the Kohen) is tithed with other animals.

If a Kohen who took a Safek may keep it, how could the Yisrael make it Ma'aser? He exempts his obligation with the Kohen's property!

Rejection (Abaye): Perhaps if a Kohen took a Safek he must return it. The case is, there are only nine other animals. Even if the Safek really belongs to the Kohen, the Yisrael has no obligation to take Ma'aser!

Retraction (Abaye): This is wrong. A Safek is not tithed.

102b: If Levi rented a house to David for 12 Dinarim for the year, a Dinar per month, they split the added month;

A case occurred in which R. Shimon ben Gamliel and R. Yosi ruled that David pays half for the added month.

(Shmuel): The Mishnah is when they come to Beis Din (for a ruling) in the middle of the 13th month, but if Levi said at the beginning of the month 'you must pay extra for this month', David must pay for the entire month;

If Levi made no claim until the end of the month, Yehudah need not pay.

Answer: Shmuel is unsure whether or not the latter phrase is binding, so we follow Chazakah. Levi is Muchzak in his property. Reuven cannot use it without proving that he is entitled to. Reuven is Muchzak in his money. Levi cannot make him pay for what he used of the extra month.

(Rav Nachman): Levi is Muchzak in his land (even if Levi claims at the end of the month, Reuven must pay).

Rav Nachman is unsure which phrase we follow. Even if the phrase favoring the renter was said last, the owner is Muchzak and the renter must pay,

Bechoros 48a (Mishnah): If Reuven's wife gave birth for the first time, to two boys (we do not know which was born first) and one of them died within 30 days, he is exempt. If she gave birth to a boy and girl, the Kohen does not receive anything.

51b: R. Chanina used to take the money and return it. Once, he saw a man lingering around after giving the money (to get it back).

R. Chanina: I see that you did not intend to give it. You acted wrongly. Your son is not redeemed.)

Chulin 134a (Rav Chisda): If we are unsure whether a (firstborn) boy was born before the mother converted, he need not be redeemed;

Rishonim

Rambam (Hilchos Bechoros 5:3): If a Kohen seized a Safek Bechor Behemah, we do not force him to return it.

Kesef Mishneh (2:6): Perhaps the Rambam holds that Rabah gave a mere Dichuy, but he agrees that we do not force him to return it.

Rambam (Hilchos Bikurim 11:8): If the Kohen wanted to return the redemption money, he may. The father should not give intending that the Kohen will return it. If he did and the Kohen returned it, his son is not redeemed, until he gives an absolute gift. After this, the Kohen may return it if he wants to. The same applies if he stipulated that he gives on condition that the Kohen will return the money; his son is redeemed.

Rambam (19): If there is a Safek whether or not one must be redeemed, he is exempt, for ha'Motzi mi'Chavero Alav ha'Re'ayah.

Radvaz: The Rambam does not force a Kohen who seized a Safek Bechor Behemah to return it. The conclusion in Bava Metzi'a connotes that we force him to return it, and Tosfos and the Rosh rule like this. The Rambam did not say whether or not we force him to return Safek redemption of Bechoros of people and donkeys. It seems that he agrees regarding people, for the Kohen did not seize the matter about which there is a Safek.

Machaneh Efrayim (Zechiyah u'Matanah 8): The Rambam does not force a Kohen who seized a Safek Bechor Behemah because he holds that Tovas Hana'ah (the Yisrael's right to choose to which Kohen he will give) is not Mamon (a monetary privilege of the Yisrael).

Rashi (Bechoros 61b): R. Chanina told the man (who expected to get his money back) 'if I would return your money, your son would not be redeemed.' Alternatively, 'even if I would keep your money, he is not redeemed.'

Question (Machaneh Efrayim, ibid.): The Rambam holds like Rashi's first explanation. If he did not intend for a gift, the redemption is invalid if the money is returned. According to the opinion that a Kohen who seized keeps it, the redemption is (immediately) valid even against the father's will! (How does returning the money undo this?) This is even more difficult according to the Rashba, who holds like Rashi's second explanation, that if he did not intend for a gift, the redemption is invalid in any case! Tosfos says that even according to the opinion that Tovas Hana'ah is Mamon, the Kohen keeps it, just he must pay the value of the Tovas Hana'ah to the giver!

Answer (Machaneh Efrayim): The Rambam holds that we do not force him to return it only regarding Terumah and Matanos Kehunah, for once they are separated they are property of Kohanim. The five Sela'im for Pidyon ha'Ben are the father's money until he gives them. The Kohen has no rights to them, just there is a lien on the father's property. If he seized them, it is theft. The father can say that he will give to another Kohen. If a Kohen seized Safek Matanos Kehunah, he can say that he seized money of Kohanim. If the Yisrael wants to take it back, he is ha'Motzi mi'Chavero Alav ha'Re'ayah (he must prove that they are not Matanos).

Rambam (20): If a woman gave birth the first time to a boy and girl and we do not know which was first, the Kohen does not receive anything. If she gave birth to two boys and one of them died within 30 days, there is no obligation, for ha'Motzi mi'Chavero Alav ha'Re'ayah.

Ri Korkus: The Rambam says 'there is no obligation' to teach that also the children are exempt from redeeming themselves when they mature.

Rosh (Bava Metzi'a 1:13): Really, if a Kohen took a Safek he must return it. Seizure helps only for one who has a definite claim. Rav Nachman rules (when there is a Safek about the extra month) that seizure does not help because the one who seizes is unsure. Even the opposing opinion does not say that seizure helps. Rather, being quiet until the end of the month is admission that he rented it for the entire year.

Poskim

Shulchan Aruch (YD 305:13): If there is a Safek whether or not one must redeem, he is exempt, for ha'Motzi mi'Chavero Alav ha'Re'ayah.