Timothy A. Crowley was born on February 14, 1831, in Lowell, Massachusetts, to Timothy and Mary Crowley. By 1850, he was working as a machinist in Lowell. By 1858, he was working as a police officer. He married Harriet Ryan on May 19, 1858, and they had at least two children: Marietta, born on October 8, 1859; and Thomas, born on December 15, 1861. By 1860, Crowley was studying law, and he owned $1,200 of real estate and $250 of personal property.
He enlisted in the Union army on April 16, 1861, and he mustered in as a sergeant in Company H of the 6th Massachusetts Militia Infantry. The regiment helped guard Washington, D.C., during the summer of 1861, and Crowley mustered out on August 2, 1861. He returned to the Union army in November 1861, receiving a commission as a captain in Company E of the 30th Massachusetts Infantry. He died of disease in New Orleans, Louisiana, on October 5, 1862.