As we reported ... police in Washington opened an investigation into Kasem's death last month at the request of his widow, Jean Kasem, who alleged members of the Church of Scientology and Casey's kids conspired to kill the radio icon for his money.

But, Gig Harbor Police concluded the standard of care Casey received from medical personnel at the behest of his children was appropriate, adding ... "There was no evidence of collusion between parties that would construe any part of this incident to be considered a homicide."

Casey's daughter, Julie, tells TMZ the family's grateful to the police for confirming what they already knew ... "That Jean Kasem’s ridiculous allegations are completely unsupported by reality or fact."

Julie adds ... "Jean has once again instigated a baseless investigation, then went on a media blitz to detract from the mountains of evidence we have compiled against her.”

As you know ... Julie and her siblings filed a wrongful death suit against Jean in 2015. They claim she removed their dad from an assisted living facility in California and took him on a 7-day journey, but when they returned, Casey had a massive bedsore that was deeply infected. The kids allege Jean's neglect led to a staph infection, UTI, and sepsis ... all of which killed their father.