They found three victims dead at the scene.
Court records indicate John Dalton Jr. was initially charged with second-degree murder in the fatal shooting of his wife, Shannon Dalton, in September 1998.
Dalton Jr. was originally named a person of interest in the case, but later a first-degree murder warrant was issued for him.
The couple - who have three children together, aged six, five and three at the time of their mother's death - had been married for five years. Her body was discovered on the floor of their shared living room. He was paroled in 2010. After that shooting, Dalton fled to Tennessee, where he was captured a few days later, according to police.
John Dalton Jr. was arrested in Tennessee on Wednesday..
They have warned people that he is considered 'armed and risky'.
Police identified the victims as 70-year-old John W. Dalton and 65-year-old Jean Dalton, who were the parents of the suspect, and 18-year-old Leonna Dalton-Phillip, who was the man's niece.
Police say Dalton should be considered armed and unsafe.
Police believe Dalton Jr. may be driving a 2015 Black GMC Terrain, with Neb. license plate UKB787, or a Red Chevy Tahoe, with Neb. license plate VRD559.