deep target, thanx for clarifying you're meaning state parks (and not city level parks). Ok. And in-so-far as state parks go, it appears you're acknowledging that detecting is allowed. And that written permission is not a pre-requisite, right ? And that your only reason for wanting written permission, is so that if you're hassled, right ?
But then you turn around and say:
.....This one particular STATE park you must have permission to hunt from the park manager..
Huh ? Where does that one park state that is a law, that permission is required ? If you're acknwledging that state-wide, this is not a mandate, then is it written somewhere, that this singular park, is an exception to that ?
How about this: I have the perfect solution to your "letter" to deflect busy-bodies: You print out the regulations showing that in fact that the rules are silent on the subject (ie.: do not forbid it). Presto, there's your "letter"
Because the risk of going and seeking "permission letters", is you may get a "no", simply on whim (like for the "remove and take" clauses that Gary alludes to, for instance). And worse yet: with multiple persons asking, then ... it might only be a matter of time before someone dreams up the notion that it's time to "make a no-detecting rule" to address these "repeated pressing questions". While the whole time, as gordonquixote points out, others are detecting no problems there.
But yes: I don't disagree that there are times when we ALL risk bumping into busy bodies. But solution, IMHO, is not to go around seeking their blessings prior-to-start (lest you get arbitrary no's, where you might have simply been ignored). Instead the solution is to avoid those types who might get their panties in a wad. Can't you pick lower traffic times ? And then just have the copy of regulations on hand (as your "letter") if someone decided to gripe anyhow ?