Ok, let's go back a step.
If you have custody more than half the nights of the year, what you should have done in Turbotax is list the child as living with you more than half the year (select "7 months" or longer), and then say that you were allowing the other parent to claim the child with a signed form 8332 (and then you give the other parent a signed 8332). Turbotax would have allowed the child to qualify you for head of household, EIC and the dependent care credit, but not the $2000 child tax credit.
Assuming you did that, and the other parent did not use the form 8332 to claim the child, you could amend and change your answer on the custody question to "no", you will not share the child with a custody agreement. That would qualify you for the $2000 child tax credit for that child, although the credit is "up to" $2000 and the exact amount will depend on your income. And, I would ask the other parent to give you back the signed form 8332 so it can't be accidentally used.
If you are the parent who did not have custody more than half the nights of the year, you can't claim the child unless you get a signed form 8332 from the custodial parent, no matter what your court order says. The IRS follows federal tax law and not state court orders.
