US Code Title 14, Part 1, Chapter 1, § 2, and US Code Tile 14, Part 1, Chapter 5, § 89 "Law Enforcement"
http://www.law.cornell.edu/uscode/text/14/2?qt-us_code_tabs=0#qt-us_code_tabs
http://www.law.cornell.edu/uscode/text/14/89?qt-us_code_tabs=0#qt-us_code_tabs
These two sections outline the Coast Guards authority as law enforcement.
The wording includes "Petty Officers" which normally would include E-4s but it is my understanding that the Coast Guard administratively regulates this authority to enlisted members starting at the rank of E-5. I may be wrong about this and they may include E-4s as well, if so my original post should then read "Petty Officers and up", instead of "E-5 and up".
The area of authority of Coast Guard members as law enforcement personnel is limited to certain defined areas per US Code Title 14, Part 1, Chapter 5, § 99, and US Code Title 46, Subtitle VII, Chapter 701, Subchapter I, § 70101.
http://www.law.cornell.edu/uscode/text/14/99
http://www.law.cornell.edu/uscode/text/46/70101
Unfortunately I do not think his status as a member of the Coast Guard nor the CGs law enforcement role will allow your relative to carry in California (or anywhere else for that matter) unless he is carrying specifically in the line of assigned duties.
-Z