A sensing system for a vehicle includes a sensor module configured to be disposed at the vehicle. The sensor module includes a sensor disposed in a housing, which includes a mounting portion and a cover portion. The mounting portion is configured to attach at a portion of the vehicle such that the cover portion is at an exterior of the vehicle. The cover portion is removably attached at the mounting portion and includes tamper resistant attaching elements such that an attempt to remove the cover portion or sensor module damages the sensor module. The sensor module may include a washer nozzle for directing pressurized fluid or spray onto a window of the sensor module. Responsive to an output of the sensor, a control determines the presence of one or more objects exterior the vehicle and within the field of sensing of the sensor.