“Should” is simply the wrong question to ask when considering whether you have a community property business. The right question has more to do with what “is” under the law. California is a community property state. This means that anything that was acquired through labor or skill during the marriage is community property. If you built your business with the sweat of your brow, but that sweat came during the marriage, the fruits of such labor will be community property. So, yes, if you worked to grow your business during the marriage, chances are it is a community property business.
Even if your business was established prior to marriage, but it grew as a result of your labor during the marriage, there is a good chance the community has at least part ownership. Below are links to some cases and code sections relevant to the community property business:
Pereira v. Pereira (1909) 156 Cal. 1., 103 P. 488.
Van Camp v. Van Camp (1921) 53 Cal.App. 17, 199 P. 855.
Todd v. Commissioner (9 Cir 1945) 153 F.2d 553