Mackenzie Shirilla's taking her conviction to the highest court in Ohio ... asking the state's supreme court to take another look at her double murder rap.

Shirilla's lawyers filed the appeal paperwork back in April, according to reports ... “there is medical evidence” that Shirilla “suffered from a pre-existing medical condition that could have caused her to black out while driving.”

The appeal claims her attorney didn't properly investigate this possibility initially.

Court docs show the first appeal was rejected because it was filed one day late. Shirilla's legal team says they only filed the paperwork a day late because of a leap year miscalculation ... and that shouldn't be grounds for the appeal to be denied.

The state supreme court has not yet ruled on whether or not it will hear Mackenzie's case.

As you know ... Shirilla is serving two 15-to-life sentences after she crashed her car into a wall and killed her boyfriend, Dominic Russo, and their friend, Davion Flanagan.

Her case is receiving renewed attention after the release of the documentary about the incident, titled "The Crash," on Netflix.