If I remember correctly, yes there were laws against this type of superstitio going back to the XII tables. However there was no 'religious police' out there looking for instances of superstitio. It would only be applied if a private citizen actually charged someone with this crime and brought them to court. At which point the praetor (I think he would be that magistrate ruling on this) could clamp down - especially if he perceived these practices to be disruptive to society.

Magic could indeed be proscribed under Roman law. In Gaius's Institutes it does seem that magic was illegal, generally conflated with ideas about poisoners. That being said, there is a dfference between legal theory and administrative practice. For example, Apuleius, a neo-Platonic rhetorician most famous today for his Golden Ass, was charged with using love magic to gain the affection of a wealthy widow. In the speech (if indeed it was a real defense and not just a rhetorical exercise) he doesn't seem to treat the charge too seriously. He starts the speech like this:

Maximus Claudius, members of the council, I was quite certain and took it as true that Sicinius Aemilianus, an old man of notorious recklessness, faced with a lack of crimes, was about to use nothing but noise to fill an accusation of me which he began before he thought it over. Obviously, anyone innocent can be accused falsely, but he can't lose the case unless he's guilty.

So it seems that it is technically actionable, but not really taken seriously in practice. And from a legal standpoint, its prohibition was more about the harm it causes than the thing in and of itself. So it is more that it is illegal to make people sick than it is to cast spells.

Now the interesting intersection between magic and law is that magical spells tend to be formulated in a highly legalistic way. Because a great number of the spells recovered tend to be by those in more humble stations (washer women, peddlers, farmers, etc) it is often suggested that magic acted as a sort of alternate legal system for those for whom the legal system generally didn't concern themselves. In general the Romans had a weak executive force and little interest in micromanaging its subjects' lives, and weren't going to send a cohort to find somebody's linens, so people had to resort to supernatural justice.

If you are interested, I would recommend Daniel Ogden's Magic, Witchcraft and Ghosts in the Greco-Roman World. He maybe focuses a bit more on ghosts than is warranted but it is a very good book.