As a point of contrast, the New Zealand police own 1 helicopter, and contract out flying light aircraft to commercial operators.
Upon saying that, they often call upon the air force for logistical support (in particular for helicopter operations, usually for drug operations, such as airlifting cannabis for destruction, not for raids).
In the US, it is illegal for the military to operate in a civilian law-enforcement context. The National Guard (state militias) can be called into civilian action by the state governor, but do not normally perform civilian tasks.
Helicopter ownership by police departments is common. Airplane ownership is less common, at least at the city/county level - the state police forces frequently have small planes.
As a point of contrast, the New Zealand police own 1 helicopter, and contract out flying light aircraft to commercial operators.
Upon saying that, they often call upon the air force for logistical support (in particular for helicopter operations, usually for drug operations, such as airlifting cannabis for destruction, not for raids).