Forty-one-year-old Darius Nauseda, from Cedar Ridge in Dungannon, admitted three charges of assaulting the officers on August 28 last.
District Judge Michael Ranaghan told Nauseda that having police officers in his own family he should have known better than to treat officers in this way when they were only doing their job.
Prosecuting counsel told Dungannon Magistrates Court on Friday that police were called by a third party to a report of raised voices at an address in Cedar Ridge.
The lawyer said the defendant answered the door to police, who noticed two females in the background, but no sign of a disturbance.
One of the females told police that Nauseda had arrived home from work drunk and she had called her sister.
Counsel said Nauseda pushed one officer and grabbed two others by the arm and wrist, while handcuffs were being applied.
A defence lawyer stressed the incident had happened at a time when "emotions were heightened".
He said one of the females was the defendant’s partner and the other was his sister.
An argument over money in a child's account which was mssing in Lithuania had started the argument, he said.
The lawyer said Nauseda was "taken to the ground" by polce and held in custody for 17 hours before being charged.
He added that the defendant was ashamed with his behaviour as he had a prosecutor and police officers in his own family.