EdSane
Yes, it is lawful to detain a person(s) you’ve witnessed committing a crime. A few points to consider. The crime has to be a misdemeanor or greater. Are you a lawyer?
Just because you believe its a crime is not necessarily fact. A police Officer can detain on the “suspicion” of a crime. A citizen can only detain based on crimes they have “witnessed”. If it is later proven that no actual crime occurred you could be liable for both criminal and civil penalties.
One other thing to consider. It is never lawful for a citizen to use lethal force on a fleeing suspect. Unless its a major offense (assault/DV), I would let the individual go. The best thing to do is memorize the perps features (anything that is distinguishing). Lock that into your mind and grab a pic if possible.