Generally speaking, it's a police officer employed by the state. For instance, you may have city officer, county officers, and state troopers. In my state, state troppers are charged with "enforcing federal and state laws relating to traffic, investigating accidents, and criminal interdiction on roads and highways."
Yes,a state police can investigate a state case.
Maryland State Police was created in 1921.
to be a police officer you need to attend a state approved police academy and be state certified in the state you live in.
In a police state, the government would control the actions of police.
It was the Pennsylvania State Police.
Indiana State Police was created in 1933.
California State Police was created in 1887.
Connecticut State Police was created in 1903.
Virginia State Police was created in 1932.
Louisiana State Police was created in 1922.
Idaho State Police was created in 1919.
Oregon State Police was created in 1931.