The Senate Rules Committee has unanimously authorized a year-long, $740,000 investigation of the Bureau of Indian Affairs and alleged mismanagement of natural resources such as gas and oil.

The investigation also will be looking into alleged fraud and malfeasance in the administration of housing, education and health programs.

The committee voted last week to approve $240,000 for the current year after Sen. Daniel K. Inouye (D-Hawaii), chairman of the Select Committee on Indian Affairs, said the investigation is a result of "reports of ongoing mismanagement of the federal government's administration of its trust responsibilities."

In answer to a question by Rules Committee Chairman Wendell H. Ford (D-Ky.), Inouye said the Indian Affairs Committee would seek another $500,000 for the investigation in 1988.

In remarks to the Rules Committee, Inouye said the allegations of mismanagement "extend to almost every aspect of the administration of Indian affairs, and include the development of Indian trust resources, and the management of housing programs, health programs, education programs, economic development initiatives, and the administration of law enforcement on Indian reservations."

As an example, he said 34 reports of the Interior Department's inspector general and an equal number of reports issued by the General Accounting Office, the congressional investigative arm, since the early 1970s estimate that the Interior Department has failed to collect approximately $5.7 billion in oil and gas royalties from oil companies.

Inouye said the Interior and GAO reports also document another $5.8 billion worth of oil and gas that has been illegally siphoned off of Indian and public lands.