Citizen’s arrests are not something authorized by either the U.S. Constitution or federal law. The extent to which citizen’s arrest is possible depends on the applicable state law. In Florida, no statute authorizes citizen’s arrest. It is allowed however under common law in two circumstances: where you witness the crime taking place or where the crime is a felony and you have sufficient reason to believe that the person committed that felony offense. “At common law, a private citizen may arrest a person who in the citizen's presence commits a felony or breach of the peace, or a felony having occurred, the citizen believes this person committed it.” Edwards v. State, 462 So. 2d 581, 582 (Fla. Dist. Ct. App. 1985).
But understand two very important things about these arrests. First, all that you are authorized to do is hold the person until the police arrive, at which time it is up to the police to decide whether to continue the arrest or release the person. That means that you can pretty well bet that if you attempt an arrest of the governor or a state legislator on the kind of crimes you suggest that they would likely decline to make the arrest and refer you to making a complaint with the state or U.S. attorney. Second, if you make an arrest for a felony not committed in your prsence and it turns out that the person is not guilty of that crime you may end up civilly or criminallly liable for false arrest.
Given that your arrest is not likely to accomplish much (aside from perhaps giving you your 5 minutes of fame on Florida news) and carries significant risk of legal consequences if you’re wrong, I suggest this is not a very prudent way to go. Instead, if you have real evidence of a crime committed by the governor or legislator, provide that evidence to state and/or attorney general.