Attention to Detail

 Working backwards...

The detective noticed a crushed-out cigarette in the ashtray.

From the lipstick residue he assumed the smoker had been female.

The amount of cigarette left unburned suggested the smoker had been in a hurry to leave.

The dark shade of lipstick, as well as the brand of cigarette told him she was a tall, brunette, had expensive taste and liked to dress well.

He noticed that the uniformed officer making the chalk outline around the body had somehow put on mismatched socks this morning.  The sock on the man’s left foot was obviously not regulation.

The detective would have to include this in his report, even though he knew the uniformed officer would be written up for the infraction.

The body on the floor was that of a tall, well-dressed brunette.
She seemed to match the detective's previous assumptions. 

On the last page of the detective's report he noted that even though there were No Smoking signs in every room of the museum, there were also pedestal ashtrays for the convenience of the patrons.   He found this to be odd, and was concerned that it sent a mixed message.

It was the detective's partner who was presently questioning the young woman who was standing over the body with the smoking gun.  He knew they would compare notes later.  He didn't want to just assume that she was somehow involved.