Authorities received reports on Sunday night and Monday morning about the dead birds near Heng Yiu House at Fu Heng Estate.
They also found a dead sparrow and 10 pigeons that looked unwell.
Some bread and bits of meat were discovered in the area, the police said, and these were sent for lab tests.
The dead pigeons were taken away for toxicology tests and vet reports.
Officers said it is unclear why the pigeons died and they were not ruling out any possibilities, including that the birds caught a virus or ate something toxic.
They said there was no evidence so far, however, to suggest that someone deliberately poisoned the birds.