Legislation is important in pubic health but we can't really run a randomised controlled trial of laws (though perhaps my next* novel should be set in a world where, at random, half the population are allowed to smoke cannabis legally and the other half aren't). So analysis of interrupted time series - before and after the legislation - becomes important. Florida repealed its motorcycle helmet law in 2000, and here's what happened.
No sophisticated analysis needed, but of course it's not always that easy.
Here is a good tutorial on the statistics of interrupted time series.
Non-statistical problems include when the 'interruption' occurred. It's rarely at a point in time, even for legislation - it takes time for people to become aware of, and adhere to, a new law; and conversely some people may start adhering in advance of the law actually coming into force.
*ok - it would be my first novel, not my next.