Clues

Depending on what kind of sleuth you're using, there could be fingerprints, a weapon, footprints. The blood itself is evidence, matching DNA against known victims to possibly find DNA left by the murderer. If the body is still present, their wounds could tell what kind of weapon was used.

Details about the crime scene that only the killer would know could be used by your sleuth to trip the killer into revealing themselves. Question everyone involved to see if anyone can not prove they weren't near the living room at the time of the crime.

In a bloody living room, the blood spatter patterns would be one form of evidence. Other things the investigators on the scene would look for is the type of weapon that was used and whether that type of weapon is still on the premises or not, and where the killer entered and exited the premises, and physical evidence like hairs, fibers and other items that would be present.

Equally important, they would look at is why the victim was in that place at that time and who else might be expected to be there. They would look at the state of the victim's various relationships with family, friends and business relationships. They would delve into his financial situation. IIn particular they would look at any situation that has recently changed in the victim's life. Any of these things could give you good story material.

Something personal that the killer dropped or it fell out of his pocket

In my humble opinion: depending on who's narrating the book, forensics may or may not matter. If it's a police procedural, they matter a lot.

I got a great textbook from a local college library called "Criminal Investigation: a method for reconstructing the past." I highly recommend it. It sure beats any of the Writer's Digest books about forensics and such.

I let a lot of evidence go unexamined until (and if) I edit my novel. It helped me write it naturally. For example: my dead person was suffocated and left in a very cold room. I discovered after I'd finished that it was unlikely that he would have been in a state of rigor mortis when the police found the body. But that really isn't all that important for the plot. Just finding his body was, and the fact that the air conditioner was turned to high on a cool day. The KILLER didn't know about the rigor mortis thing, just as killerrs generally don't know about blood spatter when they're killing someone!