Last year, more than 3,456 incidents involving drones were recorded, compared with only 1,237 in 2015, PA news agency reported.
The numbers suggest about 10 incidents per day are being logged, it said.
Drone-based complaints include invasions of privacy, disputes between neighbours, near misses with aircraft and prison smuggling, said PA.
The news agency said the total number of drone incidents was likely to be higher than the figure it had given because not every force it contacted with its Freedom of Information request responded.