You will never ever get any city person (desk clerk, gardener, etc....) to say "yes" to the question "can I dig holes in the park?" I mean, c'mon, be serious. Because even though you know that you won't leave any trace of your effort, the only word left in their mind is "holes". You will always loose that battle, as there is, undoubtedly, rules about defacing public property, or disturbing the vegetation, and such verbage. In fact, you will often times get a "no" simply asking "can I metal detect" (without even mentioning holes) simply because they envision geeks with shovels, or simply say "no" because...... you asked. I mean, afterall, the mere fact that you ask them this, infers that something is inherently wrong with you, or your hobby, that you had to ask, to begin with. Doh!
But metal detecting goes on all the time in city parks and schools, and no one cares. If you are discreet, don't leave any marks or holes, go at low traffic times (early AM, etc...) then no one tends to care. I personally never ask at any park I come to. If it's not posted, and not an obvious historic monument, then I go. But if you are skittish, look up the rules for yourself, don't ask. City codes are usually on city websites, or available for viewing on the counter at city hall. Do a key word search on "metal detecting" or whatever. If it's silent on the issue, then so be it

The reason not to ask in person "is metal detecting allowed", is because you can get someone to tell you "no", when there is no actual wording to that effect. They can simply treat your question as if you were asking their permission. I've seen that happen before where persons get "no's" at parks or in cities where no one ever had a problem before. And then you risk that same desk-bound clerk (who perhaps never gave the matter thought before, and would never have even paid attention), to all of the sudden start noticing and booting others!