Gene Hackman and Wife Betsy's Full Final Autopsies Will Take Weeks

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It'll be a while before we get the full story on Gene Hackman, his wife Betsy, and their dog’s suspicious deaths -- 'cause TMZ has learned that even with the initial autopsy, the final report will take a few more weeks.

Sources tell TMZ that after the autopsy is done by the New Mexico Office of the Medical Investigator, it’ll take 4 to 6 weeks for toxicology and other tests to come through before the final report is issued.

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Authorities have been super puzzled over their deaths -- making a note of how Gene's front door to his NM property was open when they entered for the search warrant of their house.

The…