The federal government appears to be falling far short of its collection target $25 billion in socalled "windfall profits" taxes on crude oil and gas -- perhaps because of underreporting by producers, according to official documents.

The apparent shortfall in tax collecions -- combimed with allegations by government engineers of widespread theft of petroleum from federal and Indian lands, and a California lawsuit alleging underpayment of royalties by oil companies -- has triggered a criminal investigation by the FBI.

An FBI spokesman to discuss the investigation, but its existence was confirmed by the Interior Department.

Congressional sources said the FBI probe of "hot oil" is focused on California, Colorado, Montana, New Mexico, Utah and Wyoming, which account for most of the energy production from federal and Indian lands in the contiguous 48 states.

There are no reliable estimates of the magnitude of alleged theft and underreporting of petroleum and gas extractions from these lands, but Interior has said the amount could be more than $400 million a year in Wyoming and Montana alone.

Theft and underreporting of oil and gas extractions affect federal revenues in two ways: producers escape paying government royalties, and producers pay a smaller profit tax.

Congress enacted the tax in 1980 to allow all Americans to share in the benefits to oil and gas producers when federal price controls on such resources expired.

In the first five months of this fiscal year, the Treasury Department reported collecting $6 billion in "windfall profits" taxes -- about half the amount needed to meet the federal target of $25 billion for the full year.

The Internal Revenue Service, which processes the tax returns, so far can account for only half as much money as Treasury said has been collected.

The U.S. Geological Survey, which collects the tax on certain federal leases, said in its 1980 excise tax reports to the IRS that the amount of "windfall profits" taxes collected was "none."

A Geological Survey spokesman said there was no change in the excise tax report filed for the first quarter of 1981.

Doyle G. Frederick, the survey's acting director, said the agency has reported no "windfall profits" tax collections so far because it is still developing a computer system to assume accurate tax statements.

Eddie R. Wyatt, the Geological Survey's acting assistant director for mineral resoources, said the oil producers have paid money, but the government has not yet sorted out how much is for royalties and how much is for "windfall profits."