with all due respect for dynamo76 .... no, it is not a good idea to call the park's dept, and ask for "permission". Because you might just get someone to say "no", when ..... truth be told .... perhaps they would never have even cared or noticed you (till you came in with your "pressing question"). If there is no rule prohibiting an activity, then why would a person "need permission", in the first place?
And as for gleaners advice to ask the police, this is perhaps better (because they're maybe going to actually answer with whether or not there's actual rules or laws on the subject, rather than whimsical arbitrary "permission" type responses). But on the other hand, you could get a police person to reply in some odd way, like saying "yes but you can't dig" (EVEN IF YOU MADE NO MENTION OF "DIGGING"!). Why? Because let's face it: that's the knee-jerk reaction of some people's mental impressions, and the connotation of metal detectors afterall.
But all such verbage in city laws that disallow "alterations" "vandalism" "defacing" and so forth, when you think of it .... all distinctly refer to the END result, technically speaking. So if you leave no trace of your presence (cover your spot, stomp it down, ruffle it up, etc...), then by logical definition, you have not alter
ed, vandaliz
ed, or defac
ed anything, now have you?
So I would not put myself up to the mood or potential for someone to morph other things to apply to my question. If you are skittish, look up city muni codes for yourself. If you see nothing there saying no-metal-detectors, then presto, it must not be prohibited

City charter, laws, codes, park dept. rules, etc.... are usually available on their website. If they don't have a website that detailed, then usually available in binder form on city hall front desk, etc....