What kind of rat trap? Due to ongoing problems with squirrels getting in the attic, I recently bought some old-style wooden based Victor rat traps. Modified them by increasing tension on the spring with a spacer & drilling holes in the wooden base(a few vids on youtube about this). Then used 2 drywall screws apiece to mount 4 traps on several trees around the house, baited them with peanut butter with a little dry oatmeal mixed in. Some were sprung, one not, but on the sprung ones never saw any trace of hair. I did see evidence of bait eaten on 2 traps. Somewhere we have an old Havahart trap large enough for a racoon, may try that one soon, wire it open for a few days so they get used to free goodies. I took the rat traps down today, but can put 'em back up easy enough, cordless drill & drywall screws make it fast & easy.
BTW- while the Victor rat traps should be big enough for the gray/cat squirrels, I have serious doubts about them being big enough for the fox/red squirrels. We have both, plus occasionally some black squirrels show up.
Any trapping suggestions appreciated. I *do* have suitable pellet guns &/or .22 rifle or .410 shotgun, but it's very difficult to catch 'em when I can only watch 2 sides of the house at once. They just go to the other side of the house.