You not paying them wouldn't affect the SOL, even if there was such a thing on parking tickets.
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One misconception about statutes of limitations is that people think they can disappear after being charged and that after a certain amount of time, the S of L will run and they can't be prosecuted. Not quite the way it works. Generally, if a crime has been commited and the police fail to make an arrest or the DA fails to prosecute in a certain amount of time, the S of L will run. However, if person is charged and then disapears, then it is not the governments fault and the S of L does not run. Although I doubt there is an S of L for parking tickets, if there were it would only matter is the law decided to try and ticket you after the time period in the S of L, but not run if you just didn't pay them. You could try to negotiate a settlement.
Marijuana is against federal law. Federal law supersedes state law. A person could be charged and convicted for marijuana related crimes such as possession, cultivation, distribution, manufacturing, transportation, and conspiracy.