PORTLAND — Maine’s supreme court has rejected a bid by a man convicted of killing his ex-girlfriend and a toddler to require additional DNA tests that he claims could have showed someone else committed the crimes.

Jeffrey Cookson wanted DNA tests on clothes worn by another man, David Vantol, who claimed responsibility for the killings, but later recanted.

On Tuesday, the Maine Supreme Judicial Court upheld a lower-court judge’s ruling that Cookson failed to establish a chain-of-custody showing the items hadn’t been tampered with.

Cookson was convicted of the 2001 killings of 20-year-old Mindy Gould and 21-month-old Treven Cunningham in Dexter. They both were shot in the back of the head while they were lying facedown in the bedroom. He’s serving two life sentences.