The three men sent the bullet back to the detective bureau.
Luke then went home to sleep, which isn't to say Luke was irresponsible.
Rather, with years of criminal investigation experience, he knew it was difficult to make significant progress in the case before the identification results were out.
Staying up all night at this point wasn't very meaningful.
The next day when the identification results came out, everyone else had gone out to investigate, and you were as tired as a dog, would you sleep or not?
If you didn't sleep, you'd lack energy for investigating.
If you slept, you might miss the best opportunity to investigate.
The best strategy was to conserve energy now and go to the police station early the next day.
...
Luke didn't return to his own home but went to Daisy's place, and incidentally, he gave her the documents about the Harley theft suspect.
