Our pool is our first, so we knew close to nothing when it was built, relying on the pool builder and city codes. We're in the city of Katy, near Houston but with more inspectors than policemen and firemen. A pool builder located here in Katy does not build pools in the city due to, as he puts it, excessive codes and inspections. In any case what seems to be common here is what we have. Because the pool decking is adjacent to the covered patio, there are two drains in the decking plus one in the grass near the patio. Purpose is to catch rain water and route it to the street, then of course the storm drains. Two roof gutter downspouts empty directly into the drain pipe. There is a popup cover at the end of the drain next to the curb. Also attached to that drain system is an overflow drain on the pool wall at a level about 1/3 of the way down from the top of the skimmers. Even during the hardest rainstorm, I've not seen the pool level get above the grate on that drain, so it seems to be adequate, although the pool is post-Hurricane Harvey, so it's not been given an ultimate test. In combination with the autofill, the pool level is pretty much maintained in a depth range of maybe 2 inches, give or take.
Of course local codes may or may not allow pool overflow into storm drains. Here they do. There is no way, I'd drain into the sanitary sewer system, though.