Any time I am measuring a half marathon or longer, I require police escort. If one can't be provided, the race director will ride a vehicle with a flashing light. We can't do any work on Disney property without a police escort for the highway work. They require one state and one sheriff. I'm not sure why they make the distinction, except that it may be due to the different roads we use.
Payment is always required for these escorts. I also let the race personnel handle the finances and making contact to work out who will be meeting me.
To help the police do their job well, I create the map ahead of time, sans the key points (though there is an indicator on the map for where they may land as we measure). They see the coning that will happen, and they know the roads. Like Bob, I explain exactly what I am going to do, as well. I will also talk with the officers often, when I have stopped at a mile mark, to let them know what to expect for the next mile.
Once you've hired an officer, they are working for you, so communicate your needs and they are usually very helpful.