I mean, the local police do have jurisdiction, they just aren’t going to do anything. Federal property is still within a state, and the state has every right to enforce their laws. Go shoot up a federal property, and watch as the local prosecutor and the federal prosecutor fight over who gets to put their name next to your conviction. The other closest analogue to look at is how crimes in an indian reservation can be charged by the reservation authorities, the state, or the feds.