To the poster that said all mattresses would have DNA and that this testing does not indicate they believe she died on the mattress, I disagree.
Graphic warning for that who want to skip:
There is no investigative value when compared to the money/time/risk to have people searching for and then testing a mattress to say Zahra used this mattress at one time.
They have made clear they believe this is a homicide and they are looking for a prosecutable case.
To me that means either the mattress had enough blood to show that she both died on the mattress and that there is enough blood spilled to rule her deceased without a body, OR they believe she died there and decomposed to some degree which would not show cause of death but could prove death therefore homicide.
I personally believe they think she died and laid there for some time because if we were talking about that kind of blood splatter there would be a crime scene somewhere. Blood splatter on the walls etc....
My apologies for the graphic nature of my post.
But there is just no reason for them to jump through these kinds of hoops to prove she had a mattress and her parents dumped it. There has to be more to the story.