…and as this has often been a group activity, you will want to make sure that at least one person in the group is a slower runner than you are.
If you’re seriously wondering this, though, it will somewhat depend upon the park, and will probably not be anything “official” at all.  I believe Egbert just approached a caretaker-type with a request.  In Milwaukee, I got in touch with somebody at the Parks department and explained everything, and they were nice enough to send a supervisor over there to meet us when we started.  Some city parks have clubs or interest groups who take care of them — “Friends of So-and-so Park”.
In my experience, park folks are fairly interested in the ATH concept and will work with you.  Be nice, act like you’ve got some sense, and promise to clean up after yourself, and you’ll probably be successful.
Pine (emerging from the post-Milwaukee hiatus)

oh my gosh Pine. I cant believe you said that! that is so funny. take someone slower then you. thats really great! lol

What does one have to do to get a digging permit?  I beleive Egbert got one the day of his dig, but I was told that a digging permit would have to be reviewed by a town council and such.  If one is going after one of these casques, what is proper protocol?

Wear black.
Wear night goggles.
Have the car running.
(And by all means, have the correct spot!)