Facing Criminal Charges In AZ Mall Incident ...

Jake Paul's not out of the woods yet for roaming an Arizona mall as it was being looted by George Floyd protestors ... the feds declined to prosecute him, but local authorities still hit him with charges.

Reps for the City of Scottsdale tell TMZ ... now that the feds are passing on pursuing federal charges after their own investigation, the city has decided to refile charges against Jake.

Remember, Jake was initially busted and charged with 2 criminal misdemeanors -- criminal trespass and unlawful assembly -- but the City Attorney dropped the case when the feds launched its own investigation. The City had the option of refiling.

That's exactly what happened ... sources with direct knowledge…