If anything, the Constitution PROHIBITS the type of police forces we have now. They are the equivalent of “standing armies” used to control the citizenry, which were an anathema to our Founding Fathers.
When the modern police forces were first established in the mid-nineteenth century they were challenged as unconstitutional but, as we know, the courts decided differently.
Bingo, we have a winner.......Some would say that the 10th amendment grants such authority to the stated, but Article 4 Section 2 of the constitution guarantees the citizens of each state shall be entitled to all privileges and immunities of citizens in the several states. Additionally, Article 4 Section 4 guarantees to every state in this union a republican form of government, meaning that states cannot take away individual rights.
Looking to original intent we can see that police are probably unconstitutional: http://www.constitution.org/lrev/roots/cops.htm