My 4th day starts... head to the Investigation office and what I see on my desk is a note for the murder scene and not the one with lawyers.

See pic.

Anyway to activate that event on the 4th day? Did I miss something on the last past 3 days?

No to the first question. You will need to restart or load to a save game before the area described next.

Yes to the second question. In Day 1 after you offer to supervise the arrest of the pregnant lady driver and return to your car, you are supposed to continue driving to the end of the freeway where you will automatically make a U-turn. You will encounter a motorist with a traffic violation. You can either decide to let the motorist go or stop the motorist to give a ticket. Drive to the end of the freeway and repeat the U-turn and you will encounter a different motorist each time. When you encounter the road-hogging motorist, you MUST stop the motorist and issue a ticket to him so that he will be unhappy with your decision and challenge you in court on Day 4.

I want to add to this that there's is a bug which can make it impossible to win the court case. Those motorists come in random order and if Ruiz (motorist who will contest the ticket) appears late, then the clock might be bugged and will give you wrong time. If you don't give correct time in court then Sonny loses the case. If you win or lose doesn't affect to the outcome of the game, so there will be no game over if you lose in court, but if you're perfectionist like me you end up replaying several days because of that bug. But you're safe from that bug as long as Ruiz is second motorist you'll pull over.