There is no definite source but a number of possible theories:

Theory 1: Kitty referring to a “kit” container Around the 1300s, the Middle Dutch word “kit” (also spelled kyt, kitt, or kitte) referred to a wooden tub, barrel, pail, jug or tankard. If tools were put into this container, it became a toolkit, and if medicinal tools were put into it, it became a medical kit, but if money was put into a small container, it was just known as a kit, kitte or a kitty. This theory seems to be a favourite amongst etymologists.

Theory 2: Kitty referring to prostitutes that collected poker money Another theory suggested by Willard Epsy in his book “Thou Improper, Thou Uncommon Noun” is that the term kitty arose from its use in poker. Epsy proposes that “kitty” comes from the name Catherine which is sometimes nicknamed to Kitty. Poker playing was often done in environments where prostitutes were around, and a “Kitty” was a term often applied to one of these ladies. The story goes that the poker players would toss their coin bets into the laps of the nearby watching Kittys, and thus the term “kitty” arose to refer to the pool of money. As far as I’m aware, this theory isn’t particularly favoured amongst etymologists.

Theory 3: Kitty referring to a prison-like closed box of money Kitty is an old slang-term for prison, and it could be that the term was transferred to mean a “pot of imprisoned money” because the money was not allowed to be removed until the kitty was full. The link between imprisonment of money and imprisonment of people seems like a bit of a stretch and is only a tentative explanation proposed by the Oxford Dictionary.

Theory 4: Kitty cat as cockney rhyming slang for a hat Another theory that is sometimes touted around pubs is that kitty cat is a cockney rhyming slang for hat, and since money in poker games was often tossed into a hat, this became known as the “kitty”.

Source: http://www.saywhydoi.com/money-in-the-kitty-why-do-we-say-we-put-money-in-the-kitty/