Should we get overtime on the differential we are paid for workin a night shift. My company only pays overtime on our base rate.

Extra pay for working night shifts is a matter of agreement between the employer and the employee (or the employee's representative).

As for state law, overtime is to be paid at one and one-half times the regular rate of pay for all hours worked in excess of 48 hours in a seven-day workweek, under state law.  However, some businesses may be subject to the federal Fair Labor Standards Act (FLSA) that requires overtime after 40 hours in a seven-day workweek.  No employer or employee may enter into an agreement that would violate the overtime law requiring an employee to be paid overtime.

As far as the FLSA. it does not require extra pay for night work.  However, the FLSA does require that covered, nonexempt workers be paid not less than time and one-half the employee's regular rate for time worked over 40 hours in a workweek.