Sleuthing

[Couch Potatoe]

To play the role of detective, to gather facts and information usually in the traditional [Sherlock Holmes] [inconspicuous] way.
To investigate in the manner of a detective.
A proper [Sleuth] needs to be intelligent, witty, and always a few steps ahead others. In fact, he never reveals all his discoveries or conclusions. His wisdom is his greatest asset and he needs to hide that wisdom if he expects to be hired for his services.

[Merna]

the act of discovering information about crimes or other activities, and finding out who or what is responsible for them:

[Dorothey Allen]

Careful investigation into a crime or mystery.