Non-Custodial Parent Has Warrant for Arrest

Is the custodial parent still permitted to allow the non-custodial parent to have their regular visitation with the child if he/she has a warrant for their arrest? The non-custodial parent has stated that they will not surrender and has refused to provide any contact information (i.e., current address, employer, etc.), and the custodial parent is just looking out for the best interest of the child (i.e., not to let the child see their parent arrested, and not having any way of contacting the custodial parent should the non-custodial parent be arrested in regards to the care of the child afterward).

Permitted to allow? Probably. SMART to allow...another matter, for exactly the reasons you describe. No one can predict when, where, or how that warrant might be served, risking putting the child through having to witness the arrest (which automatically entails SOME level of danger) or be taken into protective custody until you can be located, or even taken with him if he decides to go on the lam, etc. Judges don't tend to have issue with visitation being interrupted when the person trying to visit is wanted. Of course to challenge that you withheld visitation, he'd have to go to court, and standing in front of a judge with a room full of sheriff's employees usually isn't what wanted people try to do willingly.