3:10 PM PT -- According to the LAPD ... homicide detectives believe Blackstone's motive was her "frustration of being forced to provide Wendy long-term care, as well as the associated financial hardship."

Jill Blackstone, a former producer on "Jerry Springer" and "Sally Jessy Raphael" -- has been arrested for murder in the death of her sister ... TMZ has learned.

Blackstone's sister, Wendy, died in 2015 from a combination of carbon monoxide poisoning and Xanax. At the time it appeared she committed suicide that was facilitated by Jill. Wendy was blind and partially deaf, and it looked like it might have been a suicide pact, but Jill backed out and left the enclosed garage. Jill herself suffered from severe carbon monoxide poisoning after the incident and spent 2 days in the hospital.

Wendy and 3 dogs perished inside the garage. A suicide note was found at the scene that police later came to believe was written by Jill.

Law enforcement sources tell TMZ ... on Tuesday, Jill was at Johns Hopkins Hospital in Baltimore when she was arrested on a warrant for murder and 3 counts of animal cruelty.