Many years ago,when I first was married, we lived in Garden Apts.. We lived on the top floor, so the roof "was ours", ha!ha!
Okay, you wouldn't believe this, but several nites, above our bed we'd hear noise coming from above the ceiling, running, thumping, chewing and then leftover pieces of wood, I guess from when the complex was built, first the office thought it was squirrels, set traps and got them, BUT it wasn't them, this continued only at night, squirrels sleep at night, I know cause I had raised 2 who lost their moms. It turned out to be raccoons. We found this out when they were running around and fell through the crawl space pull down flap. They ran around, cops came with animal control and caught them with a snoose,caged them and away they went. What smell, when they were cornered in our room, out of fear/stress one left pee, that smelled like rotting fish, horrible, took awhile to get the stench out.
They figured the raccoons were climbing up the downspouts or from trees behind the complex, found a whole that was later fixed, where they would enter the building through the roof.
I would say it isn't a squirrel, but with critters, anything may be possible. Raccoons can be cute, but I would suggest if it turns out thats your roof dweller, call animal control, raccoons can contrat rabies and transmit the disease. In animal care/control fields most of us have had our rabies shot, as a preventative measure. But the average person usually has not or ever had the vaccination. So, let them remove it.
Well I wish you luck with finding what critter is on your roof. After seeing what the raccoons did, I'd lean to them before cats, but I have had cats but are more of a dog person. So, I wouldn't know if this is common with cats. If mice scamper around at night, it may be possible the cat is going after them.
It will be interesting to hear when you find out, let us know.

Take care,
DE

BTW
I forgot to say, the sound had a lot more weight than birds too, ha!ha! Like medium size dogs running around. I had been seconds shy of them falling through, on top of me cause the crawl space flap, was above the bathroom door and linen closet, I was ready to open the bathroom door and hubby said don't open the door, it's raccoons!! I thought he had dropped something in the linen/utility closet.