Jimmy Fowlie, a writer for “Saturday Night Live” whose sister has been missing for months, recently claimed cops told the family she’s dead … but Los Angeles police are calling that significant jump BS.

Here’s the deal … Christina Lynn Downer was last seen in L.A.’s Koreatown neighborhood four months ago … and Jimmy has been giving updates on the search for her — which included a jarring post yesterday stating cops allegedly told the family she’s “no longer alive.”

But now the LAPD is pushing back, telling TMZ … “Robbery-Homicide Division continues to investigate the disappearance of Christina Downer. Although the circumstances of her disappearance are suspicious, Ms. Downer has not been located, and her case has not been reclassified as a homicide. RHD will diligently investigate this case until a resolution can be reached.”

In his latest post, Jimmy thanks everyone for their continued support and added … “I’m gonna take a step back from social media due to the intense overwhelming feelings. Please take any info you may have directly to LAPD and not me.”

We reached out to Jimmy for comment … so far, no word back.