PORTLAND — A 49-year-old Maine man serving two life sentences for the 1999 execution-style shooting deaths of his ex-girlfriend and the toddler she was baby-sitting is asking the state’s highest court to allow DNA tests that he says might show somebody else committed the killings.

An attorney for Jeffrey Cookson will appear before the Supreme Judicial Court on Wednesday appealing a lower court judge’s ruling denying his motion for DNA testing on clothes worn by another man who claimed responsibility for the killings, but later recanted.

In denying the motion, the lower-court judge stated he had failed to demonstrate the necessary chain of custody. Cookson is arguing the court held him to a higher legal standard than required by statute.

Cookson denies killing 20-year-old Mindy Gould and 21-month-old Treven Cunningham in Dexter.