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Rodney King's fiancée Cynthia Kelley is not invited to his funeral services -- King family sources tell TMZ.

According to sources, the services will be held next Saturday in Hollywood -- but the family hasn't contacted Cynthia since the day after Rodney died ... and doesn't plan to.

We're told Cynthia hasn't made any efforts to make arrangements for Rodney -- so the family doesn't feel the need to reach out.

We're told the family is also still skeptical about Cynthia's story -- that she heard Rodney banging on the window around 5 AM Sunday and then heard him fall in the pool.

The family doesn't believe Rodney drowned on his own because -- as one source put it -- Rodney was always a great swimmer.

Some family members don't have any hard feelings toward Cynthia -- but we're told many don't want to speak to her until an official cause of death has been released.

Our law enforcement sources say Rodney's death is still being investigated as an accident, and there are no signs of foul play. Attempts to reach Cynthia were unsuccessful.

Rodney King's closest friend tells TMZ ... he's asked cops to take a closer look at King's fiancée -- because their relationship was volatile to the point King wanted to break up with her.

Damon Feldman -- who worked with King on the celebrity boxing circuit and has known him for years -- tells us King complained to him in recent weeks that his relationship with fiancée Cynthia Kelley was out of control and he needed to get away from her.

Feldman was one of the friends who called police after King's death and said he didn't believe Kelley's story.

Feldman's got a bad feeling about Kelley's explanation of King's death -- and he thinks police should take a close look at her relationship with King.

As we reported, Kelley told cops she heard Rodney banging on the window around 5 AM Sunday and then heard him fall in the pool. Cops insist they have no reason to doubt what she said.

Calls to Kelley weren't returned.