The deceased have been identified as Baijnath Mandal (80) and his daughter Badami Devi (30), Katihar Sub-Divisional Police Officer Lal Babu Yadav said.
The incident happened late last night, he added.
Mandal's wife, Barpa Devi, who received injuries, has been admitted to the Pripainty health centre in neighbouring Bhagalpur district.
Land dispute could have been the motive behind the incident, the SDPO said.
The incident occurred when two persons had come to Mandal's house at Bakiya Sukhai village to hold a discussion on a land dispute. They were allegedly angered during the course of the discussion and had shot dead the father-daughter duo.
Police have sent the bodies to Katihar Sadar hospital for postmortem, the SDPO said adding, Barpa Devi could identify one of the two persons who shot dead her husband and daughter.
Police are on the hunt for the culprits, he added.