There are a few LEO agencies that allow more, but, generally speaking, most departments only allow their uniformed officers to have a mustache...Usually only a quarter inch past the corners of the mouth...not allowed to cover the colored part of your upper lip. Sideburns not below the bottom of your earlobe.
But every department is slightly different.
"Police, at all times, should maintain a relationship with the public that gives reality to the historic tradition that the police are the public and the public are the police; the police being only members of the public who are paid to give full-time attention to duties which are incumbent upon every citizen."
-- Sir Robert Peel