I work in New Jersey, if an employee is over-paid and has not come forward for several weeks to pay back the over-payment can
the employee be terminated for being dishonest?
I think it all really hangs on how reasonable it would be for the employee to notice the overpayment. Are they hourly? Does their pay fluctuate with changing schedules? Do they earn commissions or other at-risk or changing pay types? Was the discrepancy large or small?
Whatever payback scheme you implement, if it involves payroll deductions, make sure it is legal in your state. Laws vary widely on that.
Did you check to see how this error was made? I think I would call the employee into my office and explain that an error was made and how it was made (without mentioning any names). Honesty is always the best policy. I would then ask the employee to repay the money that was overpaid and give him/her options as to how it could be repaid. The employee may honestly not know that he had an overpayment in his/her paycheck.