Was told by posting No Trespassing sign on entrance to property no person(s) may legally enter property without being invited. In addition police must also follow the No Trespassing unless illegal activity is observed or has a search warrant.
You were "told" incorrectly.
Trespassing on another person's property is illegal regardless of whether there are signs up. It also exposes the trespasser to civil liability. Posting "no trespassing" signs are one good way to ensure that passers-by realize that the property is privately owned, but so is a fence or surveying pin.
On the other hand, the police are privileged to come onto private property, regardless of whether they are invited, while they are investigating a crime. They do not need a warrant or to see a crime occur (although a higher "indicia of suspicion" is necessary to justify their invasion of a home.)
In other words, the police probably can't use your property as a short-cut, but they can certainly come knock on your door to ask you questions. The No-Tresspassing signs don't change that.
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