It sounds as though you have some specific incident in mind. If so this question would more properly be addressed to the command structure of the police agency involved.
In general terms, a police officer watching a burglarly is going to cheerfully call for his friends and, once they arrive, go arrest the burglar. This will likely be followed by beer and congratulations.
We had ten burglaries in my neighborhood in one month. Arrested for numerous burglaries, the man admitted his guilt.
The plural form of burglary is burglaries, e.g. he committed seven burglaries before the police caught him.
Burglaries of both resiodential and commercial premises are felony crimes and will be investigated as such if reported, regardless of the value of the items stolen.
If you drop out of high school the police will not investigate.
No, the police do not investigate if you drop out of high school.
However long they need to find the SUSPECT.
Yes,a state police can investigate a state case.
The police will investigate the crime. Holmes can investigate anything.
The police
The cat is the culprit. The police caught the culprit in short order.
Yes they do. Even if everyone knows that it was a suicide, the police still have to investigate to prove that no "foul play" occurred.
The police can and will investigate internal wrongdoing themselves - most agencies have an Internal Affairs Division. Also the Prosecutor's Office, or the Office of the Attorney General of the state.