Given that we presume someone dies either way it becomes murder or manslaughter – it’s kinda hard to be involved in someone dying without those charges being discussed – but that gets very much into the weeds of jurisdiction specific laws and I’m not super familiar with them anyway. Someone else can answer maybe, or maybe I’ll look it up.

What is very interesting to think about is tort law, the general case history of negligence and liability when one person harms another but it isn’t explicitly illegal. Basically the injured person or family sues someone for doing something they shouldn’t have, and it gets into really interesting weird cases like could they have reasonably foreseen the injury etc. Here’s a summary of some major tort precedents going back many years: https://www.findlaw.com/legalblogs/greedy-associates/5-classic-torts-cases-made-simple-for-1ls/

My favorite is Palsgraf v. Long Island Railroad Co. (1928) where a Rube Goldberg style chain of events caused Mrs. Palsgraf to be injured and it was ruled that the rail employee could not have reasonably foreseen all of that, so they weren’t liable.

This is a long way of saying, if you do nothing then you’re an innocent bystander to a tragedy. But if you take an action that reasonably (in this case certainly) causes injury, you’re responsible for that. You might say you’d rather have one man’s death on your conscience than a dozen, but that’s for you to meditate on in jail.

The real problem with the Trolley Problem is that it presupposes only two outcomes. In real life we don’t know what the possibilities will be and many actions are available to many people. First and foremost whoever tied the people to the tracks needs to be found and tried. Second, the trolley driver and whoever created, installed, or maintained the brakes needs to be interrogated. (Trolleys don’t generally drive very fast and they almost always have low bumpers to prevent things from falling underneath.) Finally, a number of other things had to go wrong or fail to go right in order to get into the situation: the tied people have to remain there for awhile unnoticed or unhelped by anyone until it’s too late, the trolley has to not notice things and be traveling too fast to slow down by other means, and every human between the people and trolley has to essentially freeze and fail to do extreme things like cut the power or derail the trolley or yell at someone for help. There are almost always third fourth and fifth options besides a singular person happening to stand by a singular track switch that points to certain death either way.

If it was me, I would yell for help and get myself and one other to man the switch and untie the single prisoner simultaneously. Even if we somehow fail, that action is more natural and moral and understandable to a jury than freezing up and choosing only the second worst option.

Ultimately it boils down to the jury, the judge’s instructions, and the specific wording of the law.