Let me set you straight. I'm the firearms guy at my agency. There are a couple bits of good advice in this thread.
First step is to check with ATF's NFA Branch to see if it's registered in the NFRTR. They will probably require that your agency request this information in writing. See if you need to mail a letter, or if they'll take a FAX/email (They have a "NFA FAX" email address).
If it isn't registered, your agency can register it on ATF Form 1. Do not use Form 10! It will severely limit future transfer options.
Some folks will get picky and say you can't register an existing NFA firearm on Form 1. That's technically correct, however it will cease to be a DD if you remove both the barrel and the internal cylinder from the receiver. Normally you'd want to separate those items so far apart that they aren't possessed by one person/entity, but in the case of a LE agency this isn't a concern. (FFL/SOT could do it too. Both are exempt from constructive possession charges.)
Now that it's not a NFA item, you just wait for Form 1 approval, engrave maker info, and reassemble it when the form comes back approved. It won't cost anything, because government entities are tax-exempt. Then you can sell/transfer it to any qualified buyer. The first transfer will be tax-exempt also (Form 5).
You also have the option of selling it in a disassembled state as a Title I firearm (receiver), however the receiving person (or out-of-state FFL) won't be able to receive all the parts at the same time, as that would put them in constructive possession of an unregistered DD. They could have the receiver assembly shipped to one address (like their FFL) and the barrel and cylinder shipped to another address. Then they could worry about doing the Form 1 themselves.
They'd have to do a transfer (4473) through any FFL to get the receiver, assuming they live out of state. If the buyer is a resident of your state, they could accept the receiver directly from your agency. (I would run a NCIC check on them myself if my agency was selling it).
If you go with the first option (Form 1 it as a DD), then you'd ship it complete to the out of state buyer's FFL/SOT after the tax-exempt Form 5 is approved. The FFL/SOT would then transfer it on Form 4 to the individual, requiring a $200 tax. This would be their responsibility, and it's customary for the seller to NOT pay the (second) transfer tax.
If they're an in-state buyer (resident), then the agency would transfer on Form 5 directly to them. The ATF/FBI will run their background check as part of the NFA Form 5 packet. There will be no transfer tax.