The 2nd link that Doc-beav has, is strictly about state-owned lands. So it would have no bearing on county, city, or private lands. And if you're wondering therefore about city and county where you're at (whether there's any rules), look them up yourself. Certainly the muni-codes are listed for public viewing SOMEWHERE (like the city website, etc...). If there's nothing there that says "no metal detecting", then presto, it must not be prohibited. There's your answer.
And as for the first link, that's a thread with multiple people chiming in, with multiple diff. links and observations. Just watch close for the same thing: That some stuff there may only be state lands, and not city and county. And as for things forbidding alterations, defacement, vandalism, etc..., no, I do not consider those to forbid metal detecting (even though it was the "pressing issue answer" given to some people who might have taken it upon themselves to go find a bored desk-bound bureaucrat to tell them "no"). Because when you think of it, technically, all such verbage applies to the END result. So if you leave the area exactly as you found it (no trace of your holes, pack them, stomp them, ruffle them up, etc...), then technically, you have not alterED, defacED, or vandalizED anything, now have you?
Just avoid busy-body lookie-lous & stay away from obvious sacred historic monuments, etc....