Detective Mike Logan was on 'Law & Order' from the first episode until he was reassigned (for punching a politician) in 1995. In the TV movie "Exiled", Logan was working out of Staten Island with an eye to making his return to a Manhattan precinct. This finally happened when he was assigned to the Major Crimes Squad in the fifth season of 'Law & Order: Criminal Intent'. (He also made a few appearances down in Baltimore on 'Homicide: Life On The Street', which is why he was inducted into the TV Crossover Hall of Fame in April of 2006.)
But there is very little we know about Mike Logan's personal life - he was raised by a physically abusive mother; he was sexually assaulted by his parish priest; and his girlfriend got an abortion against his wishes.
Based on his entry in Wikipedia, it sounds like his father was absent from the family for one reason or another. ("My mother beat me with one hand while she held a Rosary with the other." - so where was Dad during all of that?)
Either Mr. Logan died when Mike was very young, or he and his wife were divorced, or he abandoned the family... or "Mrs." Logan was never married in the first place.
But Mike Logan's father may have had a brother who served as a role model for a young Mike. In the 'N.Y.P.D.' episode "The Red-Headed Pigeon", someone named Logan was able to get a plaster cast of a shoe at a crime scene. I don't know if the NYPD had an actual crime scene unit in operation by 1968, or if this was done by one of the investigating officers of the 27th Squad, but Lt. Mike Haines spoke of Logan as if the other detectives knew who he was.
So I'm going to make the claim for a theory of relateeveety - this Detective Logan or CSI officer Logan was the uncle to young Mike Logan, who would have been thirteen years old at the time of that rape case. And he could have been so influenced by this uncle that when he became a detective himself, he made sure he got assigned to the same precinct, the 2-7...... BCnU!