The tower's tunnel which in real life once had vehicle traffic, is possibly closed in the game due to safety precautions against terrorism (possibly the same reasons that all the bridges were closed at the beginning of the game. That may be a reference to the mission in GTA LCSToni puts a bomb in the subway tunnel and the whole Fort Staunton neighborhood explodes). The real life building is home to many public agencies.
The building was a setting for a mission in the Rockstar video game "Max Payne".
If a very high wanted level is obtained, cops will often spawn on this building with sniper rifles trying to kill the player.