If the LEO is not there on official business, do you not have the right to ask them to leave? If there on official business, then they are the authority for the moment. You can't fairly say 'I know a murder was committed on my property, but you have no right to be here, now go...'. But if they are not there on official business and wander onto your property and sit down on your deck to have lunch by your pool, you have a right to have them leave.
Even if they are on official business, I would think that we have a right to deny entry unless they have a warrant. A person could make entry conditional on the officer disarming themselves. I can't imagine this working out well though.