Many local PDs encourage you to use their lot for CL transactions, it is a good way to go in my opinion. I would call the nonemergency number during business hours to make them aware, you can't usually call dispatch anymore because those are central to the county and no longer located at the police departments.PD, maybe: call them and ask if it's ok. Some will encourage it as a safe way to conduct such a sale, other would condemn it. I'm sure each is different.
Gun-Shop: same goes for them. Some may allow it but call and ask them first. I have had 1 instance where I bought a private party gun at a gun-shop. I was there, a gentleman came in to put a few guns on consignment, the deal wasn't yet struck with the dealer, and the guns were still in the possession of the rightful owner. I spoke up that I was interested in one of them. FFL said, "step outside the door to make the deal and I'm ok with it". So we both stepped out, I handed over cash, and he handed over the gun and went back inside to put the rest of his guns on consignment.