We have hoisted this flag on Muharram for 5 years, the family said, when questioned on the flag.
Police are investigating a family in Bihar's Nalanda, the home district of Chief Minister Nitish Kumar, after they seized a Pakistani flag from them.
The police said they rushed to the home of a man called Anwarul Haque in Kharadi colony, Biharsharif, the district headquarters of Nalanda, and took away the flag after TV channels showed the green flag with a crescent moon hoisted atop his house.
The family had already removed the flag before officials reached the place, the police said.
Sub-Divisional Officer Sudhir Kumar said the matter is being investigated, including to check whether it was actually the national flag of Pakistan.
Shabana Anwar, Mr Haque's daughter, told news agency PTI, "We have been hoisting this flag on the occasion of Muharram for the past five years".
Ms Haque is a supplier of tents and furniture on special occasions.
The opposition has attacked the Nitish Kumar government over the episode with senior BJP leader CP Thakur demanding stern action in the matter.