When the Gods are Away by Robert E. Harpold

...The annual period during which the gods vacation at Mount Olympus and ignore the inconsequential mortals, and it always begins with blood. This year's first victim is a former police officer, murdered while getting butter from his fridge. Now, Virgil Glezos, the city-state's first detective on his first case, must track the killer by inventing techniques that combine magic and technology. He is aided by a professional dance choreographer, a bio-warfare expert who doesn't want to be there, two police officers who hate him, and a priest who may or may not be trying to kill him. When Virgil uncovers something deeper than a single murder, he must quickly become the wrong person at the right time to stop the greater plot against humanity.