Investigators say the 28-year-old was attending a private party April 3 at the Hot Spot Cafe, when an argument broke out.
They say that Galstyan opened fire with a semi-automatic handgun, killing four people and injuring two others.
Galstyan was arrested in Washington state after a two-week manhunt. Galstyan and his brother Samule were arrested in the northern Seattle suburb of Kenmore, Wash.