DOes a noncustodial parent need to notify custodial parent of an out of state move within a certain period in a shared custody arrangement?

It all depends on what your court order specifically states regarding the issue. Some orders state either parent must notify the other regarding a change in their address within a specific amount of time. If your does not then no a non-custodial parent has no such restraints. But the non-custodial parent will still have to comply with the custody/visitation order as is. Meaning, if there are specific drop off and pick up times/places they must comply with them. If they want them changed to accommodate them being in a new state then they must ask for a modification.