How is zakat to be paid on a sum of money jointly owned by a couple in a bank account, when they do not precisely know the proportion of each of their contributions to it?

You and your husband can obtain a bank statement to determine the name of the depositor, the amount of the deposit, and the time of the deposit. Each of you pays Zakat on your own balance if it reaches the nisab and a year has passed over it. Neither of you pays Zakat on behalf of the other unless there is an authorization and an intention present when disbursing the Zakat.