Tru G Productions: King family (Emmerdale)

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Rodney King was not a wealthy man when he died ... and now his family is asking the public for donations so they can pay for a proper burial for the infamous LAPD beating victim.

Despite the fact King scored a $3.8 million settlement from the City of L.A. after the 1992 incident, King's family tells TMZ ... there is basically no money left over to pay for his funeral costs, which are expected to run north of $22k.

The family has now issued a statement, through their rep, Kali Bowyer, asking people to contribute to a memorial fund established "for those who wish to contribute to the King family."

King's 3 adult daughters, along with other family members, are desperately trying to come up with the cash ... but Bowyer tells us, "They need the money."

King is scheduled to be laid to rest on June 30.

As far as the mystery surrounding Rodney's death, the family says, "[We are] looking forward to a swift investigation into the death of our father, as well as we put our faith in the authorities responsible for handling the matter."

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.