Still need background check for FFL transaction after CCW?

I have heard, but cannot verify that a pistol permit in the Hampshire can be substituted for a new background check every time you purchase from FFL. Sounds too good to be true.

It is too good to be true for NH. The Brady law allows for states to submit their resident permits to be an alternative to a NICS background check when purchasing a gun through an FFL. However, New Hampshire is not on the Permanent Brady Permit Chart.

That settles that! Thanks for the answer and the link.