Gemara

(Mishnah): Two Mikva'os join only if the opening between them is at least ki'Shfoferes ha'Nod (the circumference of a hollow reed put into a leather pouch from which one draws out the liquid, i.e. a circle) in which two fingers can rotate around each other.

Mikva'os (6:9): If the wall between two Mikva'os was cracked l'Shesi (lengthwise), they join. If it was cracked l'Arev (widthwise), they join only if there is a hole ki'Shfoferes ha'Nod in one place.

R. Yehudah says oppositely (l'Arev joins in any case, but l'Shesi requires ki'Shfoferes ha'Nod).

If the wall was pierced (on top), if there is water (on top) the thickness of a garlic peel and as wide as ki'Shfoferes ha'Nod, they join.

Gitin 16a (Mishnah): The following are not connections for Tum'ah or Taharah: water being poured, or flowing down an incline, or a liquid Tofe'ach.

(Beraisa): Tofe'ach Lehatfi'ach (wet enough to wet something else) connects.

Perhaps the Beraisa discusses Mikva'os, and it is like R. Yehudah:

(Mishnah): If a Mikveh contains exactly 40 Sa'im and two people immersed in it, one after the other, the first is Tahor and the second is Tamei (some water remains on the first person, so less than 40 Sa'im remain in the Mikveh);

R. Yehudah says, if the second immerses before the first totally leaves the water, also he is Tahor (the water on the first person is considered connected to the Mikveh).

Rishonim

Rambam (Hilchos Mikva'os 8:5): If the wall between two Mikva'os was cracked l'Shesi, they join. If there is 40 Sa'im between both of them, one may immerse in either one. If the wall was cracked l'Arev, they join only if there is a hole ki'Shfoferes ha'Nod in one place. If the wall was pierced on top, if there is water (on top) the thickness of a garlic peel and as wide as ki'Shfoferes ha'Nod, they join.

Kesef Mishneh: The Rambam (Perush ha'Mishnayos 6:9) and Ra'avad (Ba'alei ha'Nefesh) explain that Shesi is vertical and Arev is horizontal. R. Shimshon (on the Mishnah) and the Rosh (16) explain oppositely.

Rosh (Hilchos Mikva'os (after Maseches Nidah) 15): We need to join Mikva'os when one of them is Kosher and the other is of Mayim She'uvim or is deficient, or both are deficient. The opening between them must be at least ki'Shfoferes ha'Nod, which is (a circle of diameter) two fingers with space so they can rotate around each other inside the hole.

Beis Yosef (YD 201 DH ha'Ba): Toras ha'Bayis says that if one Mikveh is Kosher and the other is of Mayim She'uvim, it suffices if the opening between them is like a hair, since the Pesul of She'uvim is mid'Rabanan.

Rosh (16): The Halachah follows Chachamim, who says that l'Shesi, i.e. a horizontal crack, joins in any case, but l'Arev, a vertical crack, requires ki'Shfoferes ha'Nod.

Poskim

Shulchan Aruch (YD 201:54): If the wall between two Mikva'os was cracked from one side to the other l'Shesi, they join. If it was cracked l'Arev, they join only if there is a hole ki'Shfoferes ha'Nod in one place.

Beis Yosef (DH uv'Ferush): The Rambam says that when it is cracked l'Shesi, they join regarding of the total area of the gap. R. Yerucham says that when it is cracked l'Shesi, they join only if the total area of the gap is ki'Shfoferes ha'Nod. When it is cracked l'Arev, they join only if there is ki'Shfoferes ha'Nod in one place. Some say that even though the hole must be ki'Shfoferes ha'Nod, it suffices for water the thickness of a garlic peel and as wide as ki'Shfoferes ha'Nod to connect them, like when the wall was breached on top.

Taz (58): The Shulchan Aruch did not specify if he explains 'Shesi' like the Rambam or the Rosh. Therefore, we should be stringent in both cases.

Gra (103): The Shulchan Aruch is like the Rosh.

Shulchan Aruch (ibid.): If the wall was breached on top, if there is water (on top) the thickness of a garlic peel and as wide as ki'Shfoferes ha'Nod, they join.

Taz (119): The same applies if the wall was not breached but the water flows over it.

Beis Yosef (DH u'Mah she'Chosav v'Im): The Mishnah says that two Mikva'os join only if the opening between them is at least ki'Shfoferes ha'Nod. R. Tam explains, with difficulty, that the hole must be ki'Shfoferes ha'Nod, but it suffices for water Tofe'ach Lehatfi'ach.

Aruch ha'Shulchan (175): The Rambam and Shulchan Aruch (OC 162:3) hold that Tofe'ach Lehatfi'ach is a connection for (transferring) Tum'ah and Taharah (touching water to a Mikveh), but ki'Shfoferes ha'Nod is always needed to join Mikva'os.

Question: If the hole is round, the water is the width of ki'Shfoferes ha'Nod if it fills half the hole! (How can Tofe'ach Lehatfi'ach suffice?)

Answer (Beis Yosef): R. Tam requires a hole the width of ki'Shfoferes ha'Nod. The water need not fill it. R. Yehudah says that Tofe'ach Lehatfi'ach suffices; Chachamim require like a garlic peel, whether the opening is in the wall or on top. Alternatively, whether the opening is in the wall or on top all agree that the water must fill the opening. R. Yehudah and Chachamim argue about when water flows above the wall without a breach. Most Poskim hold like this. The Rivash says that Tofe'ach Lehatfi'ach is like a garlic peel.

Beis Yosef (DH Kosav): A Mishnah says that water being poured, or flowing down an incline, or a liquid Tofe'ach is not a connection. The Mordechai says that R. Tam explains that this discusses rainwater, which ceases, but in a spring they are connections. This is like the first explanation above, unlike most Poskim.

Beis Yosef (DH Od): The Ri says that when a wall separates two Mikva'os we require a hole the size of ki'Shfoferes ha'Nod, but if there is only a mound of dirt in between it suffices to level it so the waters mix, even the thickness of a garlic peel. This is the Shi'ur for one Kidush of Mei Chatas to help for two cavities in a rock (Parah 5:8). The Rambam and R. Shimshon explain the above Mishnah like this.

Rema: The same applies if a mound of dirt was between two Mikva'os and some was removed from the top until they flow into each other the thickness of a garlic peel and as wide as ki'Shfoferes ha'Nod. A full (circle) ki'Shfoferes ha'Nod is needed only for a hole (in the middle).