The police are investigating, but Kira being a Stand user makes it difficult. Josuke's granddad and a news report talk about it in Episode 2.
Are the police investigating, though? I thought the whole point of Kira-related shenanigans in DiU up until now is that the police aren't investigating. They don't know there is a serial killer. The only reason the Duwang Gang even know there is a serial killer is because a ghost who had read the manga spoiled it for them. They don't even know he's a Stand user.
I rather thought that was the point of the scene in the gym equipment room. At the time, you think his remarks about the difficulty of getting rid of three people are about him not being strong enough maybe, but later against Shigechi he seems immensely confident that his Stand wouldn't lose to anyone. So then the alternate explanation becomes "Yoshikage Kira just wants to live quietly". No triple murder or simultaneous triple disappearance to get the police interested. Even if he killed them with his Stand, which presumably doesn't leave his DNA or fingerprints on the bodies, there would still be police, just hanging around, disturbing the tranquility of his life.