Yes, you do need to give him an 8332. The IRS does not recognize 50/50 custody. There are usually an uneven number of nights in the year and wherever the child stays the most determines custodial and noncustodial parent and, yes, you do actually have to keep a calendar if the nights are close in number between you. Only the custodial parent can claim the EIC and Child care credit. Those credits don't transfer with an 8332.
