Cops are also looking into reports that Rodney was crying uncontrollably shortly before his next-door neighbor heard a splash.
Rodney's fiancee reportedly told police she didn't try to pull Rodney from the pool because she's a poor swimmer.
Meanwhile, the coroner has completed the autopsy on King's body ... but will not announce an official cause of death until additional toxicology tests and tissue studies have been performed.
The results usually take between 4 to 6 weeks.
A rep for the San Bernardino County Sheriff-Coroner Department tells us, "There will be no final ruling as to the cause and manner of death until the requested test results have been received and reviewed in context with the autopsy findings."
TMZ broke the story ... King's fiancee discovered his body at the bottom of the pool at the couple's home in Rialto, CA on Sunday morning.
King's fiancee insists Rodney had been drinking and smoking pot in the hours before his death -- and believes his death was accidental. However, people close to Rodney are concerned she's not telling the whole story.
Stay tuned ...