My ex and I share custody of our child. Nobody pays support. Does one of us answer "no" to the question "do you have children who live at home" if we are not claiming the child?
That question is for the purpose of assigning credits (the info is not transmitted to CRA) so you can both put "Yes". By answering Yes, each of you will be able to claim any expenses (such as childcare or medical expenses) for the child without affecting benefits such as the Canada Child benefit.