Snyder announced the lowering Tuesday and said the flags will remain at half-staff until after Butterfield's funeral.
The governor said the 43-year-old trooper "gave his life in service to others."
Butterfield worked from the Hart Post. He joined the state police in 1999 after serving in the U.S. Army.
Authorities said he was shot Monday evening. Police arrested a man and woman as suspects two hours later.