How many hours per day and days per a year do police officers work and how much time off?

(in the US) Police officers are customarily salaried on the basis of a minimum of 2,080 hours of work per year (52 weeks X 40 hrs per week).

Their shifts may vary from 8 to 10 to 12 hours depending on the needs and schedules of their particular agency.

All law enforcement agencies serve varying levels of government (municipal all the way to federal) and in a country as geographically widespread as the US there is no uniformity in salary scales or vacation benefits. Each individual agency will dictate those. A new recruit will get not less than 10 days vacation per year, and a senior officer, in some agencies, may get up to five weeks (25 days off) per year.