Here is a great article from Kiplinger's. As it explains, the parent who files the FAFSA is the custodial parent. Hopefully this is the parent who has the lowest annual income so that you qualify for the highest amount of financial aid. Remember that child support and alimony must be considered when completing the FAFSA.
The custodial parent is defined as the parent with whom the child spent the majority of the 12 months immediately prior to completing the FAFSA, not the prior calendar year. It is not dependent upon who claimed the child as a dependent on their tax return as that is recognized as a voluntary act and not the definitive conclusion for determining the custodial relationship.
Be aware that FAFSAs submitted by mothers will be suspect of fraud if alimony is not included. You would think this would be changing by now, but apparently it is still something that financial aid offices can easily detect.