The "Escape Artist" has been captured many times for smuggling, burglary and other mischief. He also has more bounties than we can count.
But has he ever actually been tried, sentenced, and incarcerated?
Harcourt Fenton Mudd first appeared in Star Trek: The Original Series (TOS) and Star Trek: The Animated Series (TAS).
In Mudd's Women" 13 October 1966, Mudd posed as Leo Francis Walsh, but his true identity was exposed during a formal hearing:
SPOCK: State your correct name for the record.
MUDD: Harry Mudd.
MUDD: Harcourt Fenton Mudd.
SPOCK: Any past offenses, Mister Mudd?
MUDD: Of course not. Gentlemen, I'm simply an honest businessman.
MUDD: Blast that tin-plated pot.
COMPUTER: Full data coming on screen.
RUTH: If it can read our minds, too.
MUDD: It can't, darling. It can't. Just what's on the record.
COMPUTER: Offense record. Smuggling. Sentence suspended. Transport of stolen goods. Purchase of space vessel with counterfeit currency. Sentences, psychiatric treatment, effectiveness disputed.
KIRK: Mister Mudd, you're charged with galaxy travel without a flight plan, without an identification beam, and failure to answer a starship's signal, thus effecting a menace to navigation.
MUDD: What? My tiny ship in this immense galaxy a menace to navigation?
KIRK: You're also charged with operation of a vessel without a master's license.
MUDD: Untrue! I have a master's ticket.
COMPUTER: Incorrect. Master's license revoked Stardate 1116.4.
So clearly Mudd has been arrested, tried, convicted, and sentenced before.
In "I, Mudd" 3 November 1967, Kirk & Co. discover Mudd is the ruler of a planet full of androids:
CHEKOV: You know this man, Captain?
KIRK: Oh, do I know him. Harcourt Fenton Mudd, thief
MUDD: Come now.
KIRK: Swindler and con man
KIRK: Liar and rogue.
MUDD: Did I leave you with that impression?
KIRK: He belongs in jail, which is where I thought I left you, Mudd.
MUDD: And thereby hangs a tale, yes. But look around you, Kirk. Quite a place, isn't it? I hope you're all going to enjoy it.
KIRK: All right, Harry, explain. How did you get here? We left you in custody after that affair on the Rigel mining planet.
MUDD: Yes, well, I organised a technical information service bringing modern industrial techniques to backward planets, making available certain valuable patents to struggling young civilisations throughout the galaxy.
KIRK: Did you pay royalties to the owners of those patents?
MUDD: Well, actually, Kirk, as a defender of the free enterprise system, I found myself in a rather ambiguous conflict as a matter of principle.
SPOCK: He did not pay royalties.
MUDD: Knowledge, sir, should be free to all.
KIRK: Who caught you?
MUDD: That, sir, is an outrageous assumption.
KIRK: Yes. Who caught you?
MUDD: I sold the Denebians all the rights to a Vulcan fuel synthesiser.
KIRK: And the Denebians contacted the Vulcans.
MUDD: How'd you know?
KIRK: That's what I would have done.
MUDD: It's typical police mentality. They've got no sense of humour. They arrested me.
MCCOY: Oh, I find that shocking.
MUDD: Worse than that. Do know what the penalty for fraud is on Deneb Five?
SPOCK: The guilty party has his choice. Death by electrocution, death by gas, death by phaser, death by hanging.
MUDD: The key word in your entire peroration, Mister Spock, was, death. Barbarians. Well, of course, I left.
KIRK: He broke jail.
MUDD: I borrowed transportation.
KIRK: He stole a spaceship.
MUDD: The patrol reacted in a hostile manner.
KIRK: They fired at him.
MUDD: They've no respect for private property. They damaged the bloody spaceship. Well, I got away, but I couldn't navigate, so I wandered out through unmapped space, and here I found Mudd.
At the end of "I, Mudd", Kirk sentences Mudd to cruel and unusual punishment on Planet Mudd.
Mudd turns up again in the animated episode "Mudd's Passion" November 10, 1973, having escaped from the android planet and resumed his life of crime.
The book Mudd's Angels by J.E. Lawrence (1978) contains an original novella "The Business, as Usual, During Altercations" that ends with Mudd being tried and convicted yet again.
So Mudd has been arrested, tried, convicted, and sentenced several times during the era of TOS and TAS. Of course Mudd did not always serve the full period he was sentenced for. But apparently Mudd began serving sentences in prisons or correctional facilities several times. And the summary of his criminal record in "Mudd's Women" does not mention escape from prisons or psychiatric institutions, merely that the effectiveness of his psychiatric treatment is disputed.
However, the question might be about Harcourt Fenton Mudd in the era of season one and season two of Star Trek: Discovery, a decade earlier than TOS. It is possible that Mudd has not yet been arrested, tried, convicted, and sentenced to prison in the era of Star Trek: Discovery.
Several posts on page 50 of the thread: https://www.trekbbs.com/threads/when-did-canon-become-such-a-hot-button-issue.299400/page-501
Discuss the differences between Mudd in Discovery and in TOS. Especially post 994.