The son and daughter of Rob and Michele Reiner have broken their silence … days after their sibling Nick allegedly killed their beloved, iconic Hollywood parents in their Brentwood home.

Jake and Romy Reiner say in a statement first obtained by TMZ … “Words cannot even begin to describe the unimaginable pain we are experiencing every moment of the day. The horrific and devastating loss of our parents, Rob and Michele Reiner, is something that no one should ever experience. They weren’t just our parents; they were our best friends.”

“We are grateful for the outpouring of condolences, kindness, and support we have received not only from family and friends but people from all walks of life.”

“We now ask for respect and privacy, for speculation to be tempered with compassion and humanity, and for our parents to be remembered for the incredible lives they lived and the love they gave.”

Nick Reiner has been charged with two counts of first-degree murder … he appeared briefly in court Wednesday without entering a plea.

He also faces a special circumstance allegation that he personally used a dangerous and deadly weapon … a knife.

As we reported … Romy is the one who discovered her parents’ stabbed and bloodied bodies Sunday afternoon at their Brentwood, California home.

She told police her brother Nick was “dangerous” and should be considered a suspect.

Police then arrested Nick hours later in downtown Los Angeles without incident.

Tara Reid‘s allegations of drugging aren’t necessarily false, but right now cops say their investigation’s hit a dead end … and they don’t have any evidence to support the claims.

The Rosemont Police Department in Illinois tells TMZ … no new evidence in the case has come to light, and the case is now closed.

We’re told doctors didn’t take chemical tests when Tara was rushed to a Chicago-area hospital last month … so, they won’t know exactly what — if anything — was in Reid’s system at the time.

As you know … Tara was rushed to the hospital from a hotel near Chicago’s O’Hare Airport after an employee called 911 to report a “really inebriated” guest who was having trouble staying awake.

Reid told us she only had one drink at the hotel bar that evening … though after she was served, she went outside to smoke a cigarette. When she came back, she said a napkin had been placed over the top of her glass of wine — though she decided to drink it anyway. The next thing Reid knew, she was in a local hospital receiving treatment.

We obtained security video of Reid drinking at the bar … during which time it appears she has two drinks. Tara has maintained she doesn’t remember anything after the first — and she’s accused the media of twisting her words and attacking her even though she was the alleged victim.

Tragedy in Brazil … popular influencer Maria Katiane Gomes da Silva, just 25 years old, has died after falling from her 10th-floor apartment in São Paulo.

The 25-year-old’s husband — businessman Alex Leandro Bispo dos Santos, 40 — is suspected of pushing her from the condo they shared … he’s been arrested on a temporary order while cops probe a possible homicide.

Local reports say neighbors called police and emergency crews after hearing screams and a loud bang on Nov. 29 … and when officers showed up, Santos was allegedly found holding his wife’s body.

Investigators reviewed security footage from inside the apartment and building, and according to reports from g1 and O Globo, the video appears to contradict his account … showing Santos allegedly assaulting Maria in the parking garage, then continuing to argue with her in the elevator, at one point even reaching for her neck.