The List of Assemblymembers lists a J. H. Tibbits who represented Shasta, Modoc, and Lassen counties in 1911, and a separate James H. Tibbits who represented Amador County in 1895.
In the “Great Register of Amador County for 1894,” we learn on line 2686 (on page 36) that James H. Tibbits was a 36 years old in 1894 and born in California (as well as a miner, 5′ 11″ with a dark complexion, black hair and black eyes). This puts his approximate date of birth at 1858. However, the 1892 “Great Register of Amador County” also puts his age at 36, with the same description, which would set his birthyear around 1856.
The other Tibbits, J. H. Tibbits, who served in the legislature in 1911, completed a Biographical Index Card for the California State Library, and we learn that his full name was James Halar Tibbits and that he was born at Amador Co. on October 27, 1854. As of 1911, he was living in Redding.
At this point, it looks like the two James H. Tibbits could be related (because of their close birthyears and strong connections to Amador County). However, they could also be two separate people.