The non-custodial spouse can take the Child and Family credit under certain conditions. Please see the MA technical information release TIR 24-13, which amplifies on the conditions in which a non-custodial spouse can take the credit, which is what I assumed you meant. Note that the child in question must be a dependent of the spouse taking the credit.
You can't, as you suspect, just give the credit willy-nilly to someone else.
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