I wouldn't expect a midemeanor conviction to prevent you from going to law school. Here's a link to the page of the State Bar's website that discusses felony convictions:
The other answer gave you the link. The issue will be addressed when you fill out the papers for the fitness to study law, which is not until the 2nd year (as I recall. It has been 23 years . . .) The board will probably hold a hearing to determine if you are "fit" to study and be in the practice of law. When I was in law school, a class mate had a DWI. While he was on probation, he got a public intoxication. He was required to attend a hearing and he was allowed to practice. I am aware of another current lawyer who got a possession of marijuana case while in undergraduate. He lied on his application to law school, denying that he had any type of record. He was allowed to practice law but he was on "probation" for the first two years of practice (and had many lawyers write letters on his behalf, including 2 prominent lawyers under who he practices.)
The point is, even if the case is not one that automatically shuts you out, do not lie on your applications to get into law school, AND be prepared to have a hearing to 'splain yourself and your situation at the time of the conviction.