If you’re planning on mailing in your taxes to the state of CA past the midnight deadline PST on May 17, 2021 then you probably should file an extension for CA.
If you mail it before the deadline for CA then no.
You can also file your CA state taxes for free here, using your Federal taxes as your guideline. I believe it’s pretty easy.
https://www.ftb.ca.gov/file/ways-to-file/online/calfile/index.asp
