ARKHAM ASYLUM plays a starring role in tonight’s midseason return of “Gotham’s” debut season.

With Jim Gordon’s recent demotion/punishment for asking too many questions, we now find him in a vintage “I’m a TV detective who’s been demoted to beat cop” uniform — while trying to manage the chaos in the place that will soon be of the utmost importance to one Dark Knight.

Gordon, while making a recognizable (to Bat fans) new ally at Arkham, is also trying to solve the mystery over inmates who are receiving electric-shock therapy. Gordon is also being pushed even further apart from fiancée Barbara (who left Jim and ran into the arms of her former lover, Renee Montoya) without even realizing it.

Here are Comic Riffs’ 7 Takeaways from Monday night’s episode of Fox’s “Gotham.”

1. Catching up with the Gothamites

While Gordon deals with his new duties at Arkham, an alley-roaming Selina discovers Ivy (whom we saw very little of the first half of the season), sleeping in the streets.

Bullock — who (at the outset of the season) couldn’t complain fast enough to his captain that he wanted nothing to do with having the help of a partner, especially a green cop like Gordon — looks lost and bored without his demoted partner.

Barbara continues her affair with Montoya, having been lying in bed with her for what seems like the entire duration of the show’s winter hiatus. Whether former loves or partners in the fight against crime, those connected to Gordon aren’t doing to well.

2. Penguins shouldn’t raise taxes

The Penguin — and yes, he is calling himself that now — is feeling more confident than ever after escaping an assassination attempt from former boss Fish Mooney, and earning the trust of Gotham crime boss Sal Maroni — while secretly spying on Maroni for top Gotham crime boss Carmine Falcone.

So confident is the Penguin that he decides to go down to the docks and raise Mob taxes on the fishermen. The fishermen tell Penguin that taxes are high enough and that they won’t pay more. They call the cops on Penguin. Penguin reminds the fishermen that Maroni owns the cops — except that (look here) the cops are punching Penguin in the face and sending him off to jail at the GCPD. Penguin is lost and confused as he sits in jail, being teased by Bullock. Maroni eventually comes downtown to the GCPD (no show, by the way, has ever had so many “made men” make so many official visits to a police headquarters as “Gotham”) and bails out the Penguin. Maroni lets Penguin know that it was he who made sure the Penguin got locked up, as a lesson. He sees Penguin as getting a little too cocky for his liking, so he had to put Oswald in his place. Penguin can do nothing but give fake thanks with a look that makes you wonder whether he’ll ask Falcone to speed up Maroni’s takedown.

3. A new doctor in town

Morena Baccarin (“Homeland”) makes her debut as Dr. Leslie Thompkins, and is introduced to Gordon when she’s forced to leave the female ward of Arkham to help treat inmates receiving mystery electric-shock therapy. This meeting is interesting for two reasons:

First, we have the first meeting of two of the most important allies in Batman’s life. Thompkins, as Bat-fans know, will eventually serve as one of Batman’s greatest allies, frequently giving the Dark Knight medical attention in cases where going to a hospital could risk revealing his secret identity. She will also be one of the few whom Batman shares his secret identity with — something even Gordon won’t be able to say in his future dealings with the caped crusader.

And second, there is some major chemistry going on between these two. Let’s not forget that Barbara has left Gordon for Montoya. Gordon is alone, and now there’s this beautiful doctor whom he works directly with, who admires him for his rep of trying to be a good cop. Sparks are so apparent that the patient Thompkins is treating tells the doctor and the detective to get a room. Looks as though Gordon is far from lonely. Barbara, on the other hand…

4. Relationships (and too many drinks) on the rocks

Last we saw Barbara, she was leaving a “Dear John” note for Gordon and soon lying in bed (and having drinks) with Montoya. Flash-forward to however much time we are supposed to believe has passed since the last episode: Montoya is already realizing that she and Barbara have made a mistake. When Montoya and Barbara hook up, vices apparently come to the fore — particularly Barbara’s drinking problem. Montoya — who tried every chance she got to get Barbara to leave Jim and come back to her — realizes Barbara is in bad shape and thinks her only way back to health is to leave. Barbara is furious (or maybe just too drunk) and tells Montoya off. Somewhat desperately, Barbara calls Jim, only to find a female answering on the other line at Barbara’s apartment. It’s not what you think, though.

5. Cat-girl and Ivy Kid

After finding Ivy sleeping on the streets, Selina — knowing that Gordon is having some relationship issues at the moment — takes Ivy to Barbara and Jim’s apartment for warmth and something to eat. When Barbara calls for Gordon, Ivy answers and — sensing Barbara is not happy to hear a female voice on the line — decides to play along and make Barbara think that Jim has already moved on. Selina is on the balcony unaware. Ivy is far from her villainness future, but she’s already an expert at manipulating emotions.

Gordon eventually gets to the apartment, but Ivy and Selina are gone. He sees evidence of entry and wonders whether Barbara is back. Little does he know how that first post-breakup convo with Barbara is going to go. At least he met that nice doctor at Arkham.

6. Mystery solved — and a new villain on the loose

Gordon spends most of the episode trying to solve a mystery of murder and electric-shock treatments at Arkham. The mystery takes many turns; obvious red herrings prove not to be the culprits; and the real killer ends up being someone Gordon had initial reason to suspect, but who slips through his detective work. Our weekly villain escapes — and makes what seems to be not his last appearance.

7. No other Fish in the sea

Fish has rounded up some Gotham mobsters, trying to see who would be interested in a takedown of Falcone — which would allow her to be the new boss of Gotham crime. The monsters are fine with a Falcone takedown, but are not too fond of Fish taking over. The most opposed, of course, is the guy next in line if Falcone falls — who just happens to be childhood friends with Fish’s top guy/executioner, Butch. Fish wants Butch to change the mind of his friend, or at least see whether it’s possible. But not before Fish asks Butch whether he’s having thoughts of abandoning her for his old friend. Butch says no, but he doesn’t look so sure. And after an initial meeting with his friend — at which he is told that Fish will never be the big boss and he is offered a bigger piece of the crime pie — Butch has a choice to make. He chooses loyalty, taking out Fish’s top competition, and his old friend, with a bullet. Butch has chosen his side in the coming gang war for Gotham. He’s loyal to Fish. Which makes you wonder how soon until Fish sends Butch after the Penguin.