Where can I find accident statistics on zero gravity flights?
A reduced gravity flight is just as a normal flight but doing some stuff at a high altitude, typically between 24,000 and 32,000 feet. The stuff they do is this:


Image Source

Regarding the safety, FAA spokesman said:


  Asked whether these parabolic flights will be as safe as normal
  commercial flights, [FAA spokesman], “If they operate within the
  parameters that we set out, yes, they will be safe.”


There have not been any accidents occurred for a commercial reduced gravity flight.