In a typical city, the property line is usually behind the sidewalk, although in some older parcels that's not true. In the country, it's almost always the case that the property line goes to the road center.
Most folks have no title claim to the "street", which is dedicated to the city by the platters, hence city property.
Easy to see why the cop did what he did, and there may have been a tiny bit of legitimacy in "digging is destruction of property". Anyway, it's hard to argue with a cop; much wiser to just move on.
I wouldn't want you digging on my tree bank; I mow it and remove the dog crap from it, and so am a little territorial. I generally only detect there during street reconstruction when everything is an awful mess anyway, and no one has complained yet. Haven't found much, either, I have to say.
You could get permission from the homeowner to dig even though it's not his property; at least then they won't call the cops on you, and when they show up, you can tell them you have permission.
The foregoing doesn't make sense, but as one who makes his living out there, that's how I see it.
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