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Tyrese has a warrant out for his arrest stemming from at least one of his Cane Corso mastiffs attacking and killing a neighbor's dog ... and is in full compliance with the law as he and his legal team clear up the Atlanta matter.

Gabe Banks , of Banks Weaver Law Firm, and legal counsel for Tyrese, released a statement Tuesday ... "Mr. Tyrese Gibson extends his deepest condolences to the family who lost their beloved dog to this tragic incident that occurred while Mr. Gibson was away from his home. Upon learning of this unfortunate accident, Mr. Gibson immediately made the difficult decision to rehome his dogs to a safe and loving environment."

Fulton County Police Animal Services Captain Nicole Dwyer announced the warrant , citing negligence on the part of the "Fast & F

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