ACCIDENT REPORT: Does a trip or slip and accident report need to be filled out at the time of the fall under California law?

No, but it is helpful, and it is not required under California law.

In fact, an accident report should be requested by the injured party if none is being provided following a slip and fall causing injury.  Also, the injured party should not to forget to ask for a copy even if one cannot be provided.  Today, more and more people have cell phones with camaras, and it is a good idea to take pictures of the hazardous substance or condition for any future evidence.  I have even had clients take a photo of the accident report after filling one out when it was told a copy could not be provided to them.  Gather any and all witness information as soon as possible, and if you can take a picture of witnesses, that is also a good idea.