Is it legal for a restaurant to charge a server for a tab if a customer left without paying his or her tab?

No employer can make any deduction from an employee’s wages without voluntary written authorization to do so, signed by the employee after the particular debt or loss occurs. Even with permission, no employer can make any deduction that would bring the employee’s gross wages below the minimum wage (see Minnesota Statutes 181.79 and Minnesota Rules 5200.0090).

Thank you for your quick response! I'm printing this out and giving it to my manager.

Is it legal for a restaurant to charge a server for a tab if a customer left without paying his or her tab?

Umm, no, the employer cannot do that without your permission.

The employer can discipline you (including firing you), but they cannot dock your pay unless you say they can.

I am not saying you should be fired or that you should agree to have your pay docked. Just laying out what the possibilities are.