I don't believe the local return can be eFiled and it seems you're aware of that.  With that said, I've never tried to have an amount due electronically drawn.  I assume you can provide banking information when it's paper filed filed but I've always had my clients pay by paper check and, if they had a refund, asked it be by check as well.

I updated my reply as I always intended to say "when it is paper filed".  I inadvertently said when it's efiled.  The Local return cannot be efiled but I wish it could be.