Dealing with local cops may be a whole different ball of wax, depending on the department, or even a few individuals.
I had a gun stolen out of my truck. I called the city PD, and an officer came out, drew his weapon and searched a nearby abandoned building known to be frequented by the homeless. He then took a report.
Over a year later, the FBI was kicking in doors in another part of town in connection with a major drug ring. The kingpin of the little affair apparently had my 45 in his nightstand.
An FBI agent comes knocking on my door, wanting to know how a gun registered to me ended up in the hands of the grand pooh-bah crack dealer. The local PD had never put the gun's information, which I gave them several times including the serial number, into the system.
I truly never expected the gun would be found (which the cops told me is very often the case), but thankfully, I hang onto paperwork of all kinds and had the carbon copy of the initial police report, listing the weapon's information and the fact that it was stolen.
The agent said they were going to use the gun as evidence - the combination of the gun charges (posession by a felon and possession of a stolen weapon) with the drug charges would put him away for that much longer.
After another year, the same agent came to my home and handed me my gun back. It was a little worse for the wear, with drug boy clearly having simply tucked it in his pants (a solid stainless gun had what I'd call considerable surface rust on the left side of the frame, particularly around the grip safety), and the Feds did keep the two 13rd mags worth of Hydra-Shoks (at today's prices, I'd have wept), but I got my gun back without any real hassle and really without having to ask for it.