Class 1 and Class 2 e-bikes may be allowed where non-motorized bicycles are allowed, as long as they are not specifically called out as prohibited: California State Parks, National Forest, City/Municipal Parks, trails, paths, or other places with natural surfaces and/or separated infrastructure.
It is best to check with the specific place you are visiting to check on their e-bike policy.
Laws around E-bikes are are currently being updated. The California Vehicle Code is the foundation for all electric vehicle laws of operation. The City of Chico is updating their e-bike and e-vehicle policy. More information on E-Bike classifications can be found on the CalBike Website.