Tormented cops, and sometimes there seem to be no other kind on television except maybe for Tom Selleck on Blue Bloods, often have spells of depression.

Joanna Scanlan’s Detective Inspector Vivienne Deering (top) on No Offence, a British cop show that starts streaming Monday on Acorn, opts instead for manic.

Viv, as she’s known to her friends and colleagues, when they aren’t addressing her as “Mum,” comes across as the life of the precinct, a woman not afraid to speak her mind or command a room.

She’s firstly a cop, though, heading a mostly female team on the dodgy side of Manchester, and there aren’t a lot of laughs in the cases they land.

The new season, No Offence’s second, starts with the germination of a battle between two Manchester crime families, which naturally involves turf and money, but also has a personal aspect for Nora Attah (Rakie Ayola).

Her son died, and while there’s considerable evidence it was suicide, she prefers to pin it on rival Earl Kennedy, patriarch of the Kennedy gang.

When an explosion rocks the chapel where Nora’s son’s funeral is being held, there isn’t much Viv and her team can do to prevent retaliatory measures that soon begin to feed on themselves and threaten innocent bystanders.

Viv is joined on the front line of all this by her two closest working colleagues, Dinah Kowalska (Elaine Cassidy) and Joy Freers (Alexandra Roach), both of whom bring their own neuroses to the game.

Dinah is impulsive, and Joy is almost pathologically shy.

Equally crucial, at least in the short term, Dinah and Cathy Calvert (Charlie May-Clark) share a holdover secret from the first season: They killed Vivienne’s husband while they were investigating him in connection with a series of murders.

Don’t worry, Viv knows about it. She helped cover it up. As the second season begins, many months later, there have been no arrests even as Viv vows she will one day find the perp.  

It’s a weighty secret with which to walk around, and the aura it gives to No Offence renders mildly jarring a couple of scenes designed to give the show a little sprinkle of the comic absurd.

F’rinstance.

When Viv and Dinah are running late to a gala at which Viv is receiving an award, they have to change clothes in the back seat of the car. Because the driver is racing, he’s doing high-speed hairpin corners while they’re trying to wiggle into dresses.  

Not surprisingly, the crime war issue moves fairly soon to center stage, nudging the husband dilemma and Viv’s personality outbursts toward the outskirts.

The most intriguing twist this season, beyond the centerpiece crime, springs from Viv’s new boss, Christine Lickberg (Sarah Solemani). Christine may or may not be a match for Viv, but she clearly intends to make an effort, without becoming a martinet.

Scanlan, Cassidy, and Roach play their parts beautifully giving No Offence a lively pace as well as the refreshingly diffferent flavor that can come with having women dominate a police show.