Cops in Georgia say they can’t find Tyrese‘s killer dogs — weeks after the animals allegedly mauled his neighbor’s pet to death and investigators claim the actor isn’t making it easy.

Fulton County Police Animal Services Captain Nicole Dwyer tells TMZ … authorities have no idea where Tyrese’s Cane Corsos are, accusing him of giving law enforcement the runaround.

Dwyer tells us Tyrese was supposed to surrender the dogs last Friday, but never showed. His lawyer later told police Tyrese needed to get his affairs in order first. Adding to the drama, cops saw Tyrese post online about taking a mental health break and in that post said he was flying to Dubai until November.

Cops got a warrant and searched Tyrese’s home on September 22, but neither he nor the dogs were there. That same day, Dwyer says Tyrese’s manager told investigators the animals would be handed over, but on a 3-way call, Tyrese suddenly reversed course.

As we reported … the case started September 18, when a neighbor let his dog outside only to discover it dead minutes later from a brutal animal attack. Dwyer says Tyrese had been warned repeatedly about letting his Cane Corsos roam free … calling it “negligence” that ended with an “innocent animal” killed.

Tyrese’s attorney tells TMZ … “Mr. Gibson stands by the original statement that I provided you which reflects he is fully cooperating with the authorities in this matter.”