I work for a very large for profit childcare center in MA. I was told recently that I was not eligible for overtime because I had taken a personal day that week. Is this legal? Overtime is based on a 40 hr. work week. Thank you.

Assuming that you're non-exempt, then you're right. Overtime is about the number of hours worked in a week, not the number of days.

There is no state where an employer is required to include vacation, sick, personal, holiday or other paid leave in calculating overtime. In all 50 states, overtime is based on hours WORKED, not on hours paid.

Overtime is based on a 40 hr. work week

True. The key word being WORK. You can be paid for a whole bunch of time (vacation, holiday, sick), but only hours WORKED count towards the 40 hour a work week limit before work hours must be paid at an overtime rate.