I've seen two sides of this.
A dear friend died at home and the neighbors called the police. Fortunately my husband and I got there first and I knew where the valuables were. When the police came they opened every drawer. We didn't object, but one of us quietly followed them around and we refused to leave. After about an hour of this, they decided it wasn't profitable and left. It took 5 hours for the funeral home in Guadalajara to come for the body.
Last year when my husband had a fatal heart attack while in his car the police were the first to arrive. I wasn't found and notified until 3 hours later. By the time I got to the scene the car and his body had been taken away but the police were still waiting for me. One of them handed me my husband's hat containing his cell phone, wallet, credit cards, $3,000 pesos in cash and the Tag Hauer watch he always wore.
It seems to be the luck of the draw.