On paper, a script based on the dramatic murder of Italian fashion designer Gianni Versace in 1997, set in perma-tanned Miami and with a cast including Ricky Martin and Penelope Cruz, might sound like a recipe for the biggest slice of cheesecake melodrama you will get to see all year. Not that there’s anything wrong with cheesecake melodrama. From Dynasty to Nashville, when US dramas borrow the high-octane emotion of Latin American telenovelas and mix it up with cinematic opulence, it can be alchemised into TV gold.

You saw it glittering when Penelope Cruz, playing sister Donatella, magnificent in a peroxide blonde wig and skin-tight black leather, clomping around in high heels with the thuggish gait of bruiser in Doctor Martens, addresses a shadowy looking board room hours after Gianni has been shot dead outside his Miami palace by serial killer Andrew Cunanan. “I will not allow that man to kill my brother twice,” she hisses.

The Spanish actress doesn’t make much of an attempt to pretend she’s Italian – sniggering perhaps at English-speakers conception that they all sound the same and when all the Americans pronounce her brother’s name as ‘Johnny’. As a consequence, she reminds you of her wonderful she was in the same late 90s period in the films of Pedro Almodovar. Ricky Martin turns out to be a revelation as Gianni’s partner, vilified and shut out by both family and the police.

The Assassination of Gianni Versace is not just an excuse for some great fashion and Latin passion though but a real horrific tragedy, overshadowed in history by the death of Princess Diana only a month later. Edgar Ramirez gives Versace a poetic tenderness that makes you feel the senseless waste and brutality of his murder. But it’s Darren Criss who steals the show as the real American Psycho (with plenty of nods to the Mary Harron’s film) dissembling and deceiving with alarming ease, dancing to Phil Collins, his eyes flashing behind his preppy glasses.

The first American Crime Story series, The People v O. J. Simpson combined ersatz performances with an acute dissection of the growing fault lines in American society over race and the power of celebrity.

The second series suggests there will be similar analysis of how painfully and dangerously closeted homosexuality was and how glamour and money circulates and distorts passions like drugs. But without a long court case, the exploration this time seems more psychological than sociological – what drove Cunanon to kill Versace? Did he know him? The confabulation of fact and possible fiction and glamorisation of Cunanan, despite the beauty and drama, might make this slice of real life harder to swallow.

The Assassination of Gianni Versace: ‘A new American Psycho’