As an aside, if the parents get along reasonably well, it is always worth calculating taxes both ways - Dad gets the exemption and Mom gets the exemption and then agreeing to what ever is the most practical.
For example, let's say Mom is CP and if we calculate taxes with Mom getting the exemption:
Mom gets $1,000 refund
Dad gets $0.00 refund
Now, if we calculate it the other way (give Dad the exemption):
Mom gets $0.00 refund
Dad gets $2,000 refund
So, even though Mom doesn't legally have to give Dad the exemption, they might work out a deal where Dad gives Mom $1,500 in exchange for her signing the 8332 form. Each parent would be $500 better off in that scenario.
This scenario is reasonably common when one parent makes considerably more than the other - OR in situations where CP makes enough that the deduction has phased out and isn't worth anything to them.
But if the two can't sit down and reasonably discuss it and be open about their finances, I'd probably just stick with the IRS rules unless there's a court order that says that CP has to sign an 8332.