Can I say I am a non custodial parent if I claim my daughter every other year on taxes?

[ColeenD3]

Whether or not you claim her has nothing to do with being a custodial or noncustodial parent. 

Custodial parent and noncustodial parent.   The custodial parent is the parent with whom the child lived for the greater number of nights during the year. The other parent is the noncustodial parent.

  If the parents divorced or separated during the year and the child lived with both parents before the separation, the custodial parent is the one with whom the child lived for the greater number of nights during the rest of the year.

  A child is treated as living with a parent for a night if the child sleeps:

• At that parent's home, whether or not the parent is present, or
• In the company of the parent, when the child doesn't sleep at a parent's home (for example, the parent and child are on vacation together).

Equal number of nights.   If the child lived with each parent for an equal number of nights during the year, the custodial parent is the parent with the higher adjusted gross income (AGI).