Does CSRMA cover liability for personal autos when used on District business?
The employee's personal auto policy pays all liability claims first, then CSRMA provides excess coverage once district deductible satisfied.
Do I need to tell CSRMA about a new vehicle the District purchased?
Only if you require auto physical damage on the vehicle or you have your auto liability in the PIP. If you only need liability and are in the pooled program, coverage is on blanket basis and you don't need to report it.
All employees' drivers licenses should be checked every year using the DMV pull system.