There was a game approximately 12/13 years ago: 2d Pixel art Style, sidescroller, puzzle/investigation game.
You play as a stereotypical detective always start in your apartment and had to find a certain criminal. The game consisted of several accesible areas you could move in relatively freely, there was a market and some kind of back alley with crates and stuff plus others I dont remember. In these areas certain items could be found which were clues or tools and you could talk to most npcs in an investigative manner. Afaik there also was a day/night cycle and you had a time limit to find the suspect, who could basically be any npc.
I hope that is enough info for you guys and you can help me find what I am looking for.