Can local police arrest someone in a federal building or on federal property?

It depends. There are a couple of factors: (1) The jurisdiction of the federal building, (2) the arrest charge, (3) are the local cops aware what they're arresting for. 1. Jusridiction: There are several types of jurisdiction depending on the "level" of the federal facility. Most federal facilties allow concurrent or proprietary enforcement which allows the locals to make the arrest. 2. Arrest Charge: Generally, arrests that occur on federal property are usually covered under Title 18 of the US code or 41 of the CFR. Here's the nice thing: if an offense that occurs on federal property is not punishable by federal law, the "Assimilative Crimes Act" allows the state law to be used. Example: If someone committed a robbery in the parking lot of a federal building, the locals or feds can use the state's robbery law if it's not listed in the federal law. 3. Most local cops do not know what violation has been committed or under what jurisdiction. Most of the time the feds (Federal Protective Service -FPS) are notified. They are the uniformed law enforcment division of most federal buildings.