If an employee asks for time off from work rather than pay for overtime hours worked, can a company grant this request?

It depends.  Generally, overtime is due whenever an employee who is not overtime exempt works more than 40 hours in a workweek.  (A few states require the payment of overtime if an employee works more than 8 hours in a workday).  Overtime is paid at one-and-one-half time the employee’s regular hourly rate (i.e., an hourly employee who is paid $10 per hour would be entitled to $15 for each hour worked in excess of 40).

Because Federal law and most states base the right to overtime pay on the workweek rather than the workday, an employer could give an employee time off during the same workweek (such as a late arrival or early departure) to ensure that the employee does not work more than 40 hours in the workweek.  This doesn’t apply, however, to those states requiring payment of overtime based on the workday.

But if the employee wants to take off time in a different workweek, the answer is “no.”  Private sector employers are not permitted to give employees compensatory or “comp time” in lieu of overtime pay.  (This is unlike in the government employment context where comp time is permitted under certain conditions.)