I had a similar idea at one point.
The player was a detective/Private Eye staying at a motel, and if his services were needed, he'd receive a letter under the door. The player would then investigate various locked-room murder scenes. They'd have a list of suspects to consider as directed in the first contact letter, and would have to deduct it based on evidence they can collect by interacting with the environment (albeit, not moving anything to disturb evidence and for fingerprinting).
What made mine a little more difficult was that you could also be hired for other purposes, such as messing up a crime scene, thievery, bribery, bombmaking, etc. In the case of judging how well of a job the player did, they also received a newspaper at the start of the day (back at the motel room) alongside their letter. Behind the newspaper and more script based, messing up a crime scene used binary values which, if totalled over certain amounts, would dictate an altered outcome.
Doing a better job meant more money, which puts food on the table. More money means the player can use a phone to order furniture, meaning going out for amenities decreases and lessens the possibility of being caught depending on how notorious you were. For example, buying a fridge means refrigerated goods and less shopping.
The way I was to present the deduction however, was somewhat restrictive. The player, at his motel home, would lay out all the evidence collected (which was stored in the inventory) on a table. This of course, just meant SetEntityActive("evidence", true); on preplaced assets, then questions such as "What was the murder weapon?", "Were there any fingerprints?", "What was the motive?" popped up as messages, and you choose from what's on the table.
It is definitely feasible. Just remember you're more likely to end up with a visual novel than a "game", so make an effort on your story, perhaps the murders/crimes eventually lead towards the larger one where you can make use of older case results/evidence?
If you have not already, and you're able, play some Ace Attorney and take note of how investigating works. Or watch a few playthroughs of
Ace Attorney: Spirit of Justice for the out of courtroom investigation.
My main constraint was the lang file and the newspaper. I know of potential, untested ways to overcome it, but it means a full conversion mod and a fair amount of testing. :3
If you have questions, feel free to ask!