Child support laws in every state are based on Federal laws to some
extent. I know of no place in the US where a man (or woman) is exempt
from paying child support because of no visitation.
And, let me point out there are two sorts of refused visitation. The
first, and most rare, is the court rules the non-care parent has no
legal rights to visitation. In almost all states today, there has to
be really good reasons to completely withhold an access (visitation)
order. And, rumors of universal unfitness by certain extremists do not
stand the light of a court hearing.
The most common type of refused visitation involves a legal order for
access, and the custodial (or primary care) parent simply refuses to
honor that visitation order.
Let me say, though, that a person whose legal rights are being
violated, if he/she does everything right can indeed win. The
percentages are low, but it can be done.
There is even an argument based on real life experience that
attempting to visit children in the face of such hostility is very
difficult, and may be harmful to the children. Constant hostility is
not good for children. Each case is different.
When absent parents have regular contact with their children, support
is much more likely to be paid. Just on economic reasons, it would
benefit our society to make it unthinkable for vengeance withholding
of access. At this time, I have found most people really believe the
custodial parent has the legal right to decide if access is provided
or not. This is not true at all, but the bias makes it hard to deal
with the problems of refused visitation.
And, kids who feel the absent parent still cares for them tends to be
much happier and well adapted.
One thing I learned is that many men do not visit when they might,
because of the extreme emotional pain involved in rare visits. I also
think routine counseling should be available to absent fathers to
coach them through the pain.