Jersey City to Snooki -- We're Not Afraid to ARREST Your Ass!

Snooki and Jwoww will be on some seriously thin ice when they begin shooting their new reality show in Jersey City ... because the cops will be assigned to watch their asses AT ALL TIMES.

TMZ has learned ... officials in Jersey City refused to a grant a permit to shoot the show UNLESS they agreed to some seriously strict rules.

1) The show must allow at least four Jersey City PD officers to be stationed at Jwoww and Snooki's home at all times.

2) The cops will stay with the cast and crew when they leave the home. Cops have agreed to keep an appropriate distance from the operation, so they don't get in the way of production.

3) If MORE cops are called in to handle an incident due to events related to the show, producers MUST reimburse Jersey City for all related costs.

Officials have also made it clear ... cops are taking the situation very seriously and will take action ... even on the cast ... if any state or city laws are broken.