Is my boss allowed to do this?

It's legal and go for it on almost EVERY retail store and other companies. In many extra jobs you and have on obstructed the trunk connected with your car.

It's not embarrassing unless you are caught stealing, also people know that is partial a technique check, because don't take it personal.

Of aqueduct they still need your consent; you bottle refuse if you want, but you can be legally fired.

edit

I relive a fancy retail shop where the assistant producer convinced the store owners to stop the money inspections (to employees and managers).... a scarcely any weeks later that same help mangers traverse exhausted with ALL the store's financial in HER bag, she disappeared and was never caught.