You do not need to "check in with the police" in the US. Even if you have some interaction with the police, in most states local and state police do not care about your immigration status. If you take flights, TSA also generally do not care about your immigration status. However, the CBP does operate immigration checkpoints within 100 miles of the border. If you travel close to the border and run into one of those checkpoints, then you being out of status (with no pending application for extension/change/adjustment of status) is a big problem.