Is overtime mandatory if you work overtime?

Yes. Under the law, an employer can dictate the employee's work schedule and hours. Additionally, under most circumstances the employer may discipline an employee, up to and including termination, if the employee refuses to work scheduled overtime.

However, for all hours worked over eight hours in any workday and over 40 hours in the workweek, the employee shall be entitled to receive one and one-half times the employee's regular rate of pay for all hours worked in excess of eight hours up to and including 12 hours in any workday, and for the first eight hours worked on the seventh consecutive day of work in a workweek.

No, overtime is not something you are required to work, at least by United States law. You may work for a company who has a policy or work rule that requires you to work overtime, but your employer cannot make you work overtime unless something like a policy or work rule applies. If your employer has a union you could be required to work overtime since it would not be uncommon to have a phrase in a collective bargaining agreement that says "all overtime required will be worked by the employee." In this case you would be required to work it, under the labor agreement terms, because of the labor agreement.

One interesting point about the law, is that an employer, at least under Fair Labor Standards Act, can work employees as many hours as they wish provided they pay them time and one half for all hours over forty.