NYC Shooter Traveled Across Country Before Killing 4 with Assault Rifle

27-year-old Shane Tamura drove across the country from his residence in Las Vegas before opening fire in an NYC skyscraper and murdering 4 people, including an NYPD officer, Monday night.

Law enforcement sources tell TMZ ... he was in Colorado on Saturday and drove through Nebraska and Iowa on Sunday before landing in New Jersey. He was in Columbia, N.J. as of 4:24 PM Monday ... and by 6:28 PM, a 911 center began receiving calls of an active shooter inside a building at 345 Park Avenue on 52nd Street.

NYPD Commissioner Jessica Tisch revealed in a presser Tamura exited a black BMW carrying an M4 assault-style rifle in his right hand. He opened fired as soon as he entered the skyscraper’s lobby, shooting and ultimately killing NYPD officer Didarul Islam, a father of 2 with another child on the way.

The cold-blooded killer then fatally shot a woman hiding behind a pillar, plus a security guard taking cover behind his desk, as he made his way to an elevator. A second man was also shot in the lobby, per his own statement from the hospital.

Tamura stunningly allowed a woman to exit the elevator before he hopped in and rode it to the 33rd floor, which houses Rudin Management. He riddled the air with more bullets, killing one more person, before walking down the hallway and ending his own life by shooting himself in the chest.

In addition to the 4 killed during the heartless act of violence, 1 person was wounded and in critical condition at the hospital as of Monday evening. An employee of the National Football League -- whose corporate headquarters is in the attacked building -- is also injured, according to NFL Commissioner Roger Goodell. Four other people were being treated for minor injuries from their attempts to escape the hail of bullets.

Tamura's motives are still under investigation, but Tisch confirmed he had "a documented mental health history."

A source told CNN Tamura left a suicide note in his pocket detailing his grievances with the NFL and claiming he suffered from CTE, a disease linked to head trauma -- but law enforcement officials have not publicly confirmed. He reportedly asked to have his brain studied in the letter.

Police found a loaded revolver, a rifle case, ammunition, magazines, a backpack and prescribed medication in his vehicle. No explosives were uncovered

The building at 325 Park Avenue is also home to global investment firm Blackstone, tax and audit firm KPMG and a Bank of America center.

Officer Islam is being hailed as a hero who "made the ultimate sacrifice" in the line of duty.