You have to separate what are your court ordered legal responsibilities from your tax rights according to the IRS. The IRS doesn’t concern itself with your dissolution agreement and so you can, as the custodial parent, claim the child with all of the tax benefits.
Whether the father can get any tax benefit from claiming the dependency doesn’t matter. If you are breaching your legal agreement he, of course, can take legal action against you.
You should know that even if you allow him to claim the dependency (which you should do by giving him a signed form 8332), you will still receive earned income credit, child care credit and can file as Head of Household if otherwise qualified. The IRS will give you those benefits even though your agreement reads that you don’t get any tax benefits.
