Can I Be Changed With Trespassing For Using A City/town Street That Is Part Of A Retirement Community?

Title should be "can i be charged" not changed.
This is in the northeast US. I live near a great public trail network that I use for running and biking. The fastest way to get to those trails is to cut through a retirement community, which has trail access.
The community has tons of signs that say "Private Property No Trespassing" or "For Residents and Invited Guests Only". I have seen our City/Town Department of Public Works vehicles maintaining the roads in the community, and they plow the streets in the winter.
If the municipality maintains the roads, aren't they free to use to the public? Can I be charged with trespassing for running or biking on them? I dont know if there is a way on a map to know if a road is public or not.
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