It would be in the sense of "algo relacionado com..." so, the handkerchief murder" could be translated into "o caso da morte relacionada ao lenço/o caso do lenço...etc" (caso policial digo).
Handkerchief here would mean that the murder is somehow related to a handkerchief, one example is that of Sylvester Meder. He was 20 years old, and was talking to several boys near his home, when one joked about his fancy handkerchief, then they ended up fighting and he fell to the sidewalk, dying from brain injury.
The role of the handkerchief here, is that anyone would recall that the fight broke because a joke about the handkerchief, the cause and origin of the contention between the parties.
Other example is that of the "bagel murder", the case of a man that died and two of 3 of his sons inherited the lucrative bagel store. The one left cut out attacked and murdered his mother and sister (that had nothing to do with the matter). The bagel store issue was what evoked the whole story to the public opinion.
In Australia a man murdered a partygoer with a pair of scissors, the newspapers mentioned it as the "the scissor murder" (the pair of scissors was the tool used).
In another case was known as the "nanny murder" in which the nanny was the agent/perpetrator of the murder.
So, the word that is related to or that first comes to mind in such cases is the adjective to describe the situation/the case.