It doesn't matter (subject to a very small exception).
Child support laws are very similar from one U.S. state to another because states have to meet federal standards to be eligible for certain kinds of federal funding. And, child support orders are binding even if the person obligated to make child support payments doesn't live in the same state as the state issuing the child support order.
Under those guidelines child support is based upon the father's income, the mother's income, the number of nights the child spends with each parent, and certain extraordinary expenses or in kind payments in lieu of child support. The definitions of income used, generally speaking, track those of federal tax law, which are incorporated by reference in state child support statutes, rather than state specific property and income concepts. But, there could be isolated cases where most income is derived from the property of a married person, where state community property laws could modestly tweak the amount of a parent's income.
Property ownership is not a factor in the amount of child support that is owed (in all but the most extraordinary cases that justify a departure from the child support guidelines, typically with uber-wealthy families), so it doesn't matter if the state has community property or not.
The laws of the child's "home state" as determined under the Uniform Child Custody Jurisdiction Act and Parental Kidnapping Protection Act governs which state's law governs child support determinations and which state's courts have jurisdiction to enter child support orders regarding a child.