LOS ANGELES — Rob Reiner’s addict son Nick was officially charged with two counts of murder Tuesday for fatally slitting the throats of the iconic director and his wife over the weekend — and could potentially face the death penalty if convicted, ​authorities said.

The 32-year-old ne’re-do-well nepo baby will face two counts of first-degree murder ​”with a special circumstance” in the disturbing double-slaying that’s led to Hollywood heartbreak,​ according to the Los Angeles District Attorney’s Office.

Execution in California can only be sought when a person is facing charges of murder with special circumstances, which in this​ case involves the fact that there were multiple victims,​ DA Nathan Hochman said.

“Like any case, ​[prosecutors] will take the thoughts and the desires of the family into consideration in making” ​a decision ​about seeking execution, too, Hochman added.

“Prosecuting these cases involving family members are some of the most challenging and heart-wrenching cases that this office faces because of the intimate and often brutal nature of the crimes involved,” he said during a Tuesday afternoon press conference.

Even if prosecutors pursue the death penalty, Gov. Gavin Newsom ​has had a moratorium ​in place halting all executions in the Golden State ​since March 2019.

Life in prison would be an alternative option upon conviction.

Authorities meanwhile admitted at the press conference that they are still working on nailing down key details in the case — including the victims’ time of death and even potentially finding the murder weapon.

“As to where and how the weapon was located or will be located, that will actually be evidence that will be presented in court​,” Hochman said.

The coroner is still attempting to pinpoint a time of death, but prosecutors believe two were killed sometime early Sunday morning.

“I’m sorry​, we don’t have that kind of specificity​,” LAPD Chief Jim McDonnell said. “We’re waiting for the coroner to try to determine the best they can.”

Law-enforcement sources told TMZ it appeared the pair were dead for hours – ​with rigor mortis already setting in​ when their bodies were found. Rigor mortis can typically begin two to six hours after death.

Rob, 78, and his longtime wife, Michele, 70, were found dead inside their Brentwood mansion by their daughter Sunday afternoon, according to authorities and law-enforcement sources.

LAPD Detectives Chief Alan Hamilton said the LA fire department was initially called to the scene before cops reached the Reiners’ home, paving the way to a homicide probe.

Nick, who’s battled drug addiction and had a complicated relationship with his father, was arrested Sunday night and has since been in custody.

Nick was tracked down to and taken into custody near Exposition Park, officials said.

Video obtained by The Post shows a police vehicle and then cops get out of the car after cornering the suspected stabber.

His arraignment was expected Tuesday, but his celebrity lawyer, Alan Jackson, told reporters outside the courthouse his client was not medically cleared to make a court appearance.

Nick and his parents got into a heated argument at Conan O’Brien’s holiday party in the hours leading up to the couple’s slayings, sources have told The Post.

Besides Nick, the couple has two surviving children, son Jake Reiner and Romy Reiner.

Hochman began allowing his staff to pursue the death penalty in “exceedingly rare cases” earlier this year after his predecessor, George Gascon, banned the practice.