I don't know if this is common knowledge yet, most people I play with didn't know this.
When a kill occurs inside a room that is visible at the Admin table (on most maps: anywhere that isn't a corridor) you can actually see that a kill has happened by noticing how a character quickly jumps on top of another. This is a distinct animation and differs from the animation shown when a player enters/leaves a room.
I have won so many games as crewmate by hogging the Admin table, paying attention to kills and immediately proceeding to report the body.
During discussion (if the killer didn't cross your path on your way to the body), simply ask for everybody's positions, and most of the time, the game ends right there. Experienced players won't lie about their location, as this can easily be disproven by other players.
If three players are in a room and a kill occurs without an immediate report, you can assume that both players left alive are Impostors, which can net you an instant win once you've established everybody's positions.