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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. Play video content

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

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