You cannot enter the same child on two tax returns. If all of you are living together as a family then only one of you should include the child on your tax return. The other parent files as Single and does not enter anything about the child.
If you are living apart---post back---the answer will be different.
You should enter the child but also answer Yes to the question about the child being claimed on someone else's tax return.
@bob_cutler If the parents and child are all living together, your reply is incorrect. If they are living together as a family, the child can only be entered on one parent's return. If they live apart, that is the situation in which one parent can say that the other parent will claim the child. If parents are never married or divorced and are sharing custody, the custodial parent can still file as Head of Household, get earned income credit and the childcare credit. The "non-custodial" parent can claim the child and get the child tax credit. But you have to say on the return that there is a written agreement. That agreement---Form 8332---is used by divorced or never married parents who do not live together with their child.