I don't know about your house, but ...
... If you are carrying a weapon in your car they can search your car to verify that the weapon is unloaded, in a locked container or the trunk, and that ammunition is in a seperate locked container. This can be done without any other reason, probable cause, or warrant.
They may not search the gun for a serial number. However, if they happen to see the serial number they may call it in to see if the gun is stolen. And if the serial number is accidently seen and is altered or scratched out you get a free trip to Felonyland.
Clinging to my God
and my guns!
Then said he unto them, But now, he that hath a purse, let him take it, and likewise his scrip: and he that hath no sword, let him sell his garment, and buy one.