In New York, a court is likely to find the $30,000 in cash was commingled with marital property once deposited in the joint bank account. In fact, in New York, the act of putting money in a joint bank owned by two spouses actually triggers rebuttable presumption that the funds belong to those whose names appear on the account. if one of the depositor placed the total amount of funds into the joint bank account, the presumption arises that during the lives of the parties, the one who contributed the funds made a gift of one-half of the funds to the other party.
Although this is not necessarily the end of the story, once the presumption is in place, the party seeking to rebut it must carry a heavy burden. Absent clear evidence to the contrary, the opening of an account in the joint names of the husband and wife implies an intention that the spouses were jointly interested in the accounts. Unless evidence clearly shows otherwise, the spouses interest in the account is presumed to be equal.
In the end, in a case such as this, unless additional facts came to light, it is very likely a court in New York would find the $20,000 to be marital property subject to equitable distribution.