(Note that the official number of that form is RPD-41367, not PTW-D.)

Yes, if there's an amount on Line 14 of the NM S-corp return, NM will expect an RPD-41367. Lacerte will e-file the form if you check it off in Screen 1. 

Right-click Jump to Input will show you where to enter overrides to get the presentation right, so that Line 2 is equal to Line 3 on the RPD-41367, which are equal to Line 14 on the NM S-corp return. Sure would be nice if there were a checkbox that said "pay the NM franchise tax and distribute the rest of the withholding prorata to the shareholders."