The House-Senate conference committee resumes work today on President Carter's proposed crude-oil tax, with the major oil companies and independent producers bitterly split over how much of the levy each should pay.

In the face of heavy lobbying by the majors, the trade association for the independents fired off a salvo yesterday, accusing the big companies of making misleading statements and warning that production will suffer if the big producers get their way.

Separately a coalition of groups that stand to benefit from a spate of Senate-passed tax credits for alternate fuels also held a news conference to muster support for keeping their tax breaks in the bill.

The dispute within the industry centers on a Senate-approved provision that would exempt most independent drillers -- and those who lease land to them -- from the tax, at the expense of the majors, who then would have to pay more.

The majors are complaining that this would lead landowners to lease only to independents, shutting out big companies. The House version of the bill has no such provision.

The battle is a fierce one because the provision involves about $42.5 billion in anticipated tax revenues between 1980 and 1990 that the majors fear they may have to pay if the independents are exempted.

The conferees tentatively have agreed to shape the overall crude oil tax so it raises $228 billion in new revenues over 10 years, and are now to decide exactly how to do this. The House bill would raise $277 billion, the Senate version $178 billion.

C. John Miller, president of the Independent Petroleum Association of America, called the rift between the two groups yesterday "the most serious rupture that I'm aware of" in the industry's history.

Miller told a news conference that "if the major oil companies had fought as hard against the [entire] bill as [they have] against this provision, we wouldn't be in this bad shape right now."

Meanwhile, two key House conferees served notice they may seek to scrap the present bill entirely and replace it with a straight severance tax of 15 or 25 percent on each barrel of oil produced.

The lawmakers, Reps. James R. Jones (D-Okla.) and W. Henson Moore (R-La.), say their proposal would be simpler than the House-Senate bill, which would tax various kinds of oil differently, yet would raise the same revenue.

Separately, the staff of the Joint Committee on Taxation circulated option papers among panel members showing how various provisions in the bill could be altered to shift the tax burden while still raising $228 billion. b

The options include raising the tax rate on slowly newly discovered oil to 65 or 70 percent, from 50 percent in the House bill, and 10 percent in the Senate version, and juggling the rates for tertiary and heavy oil as well.

The news conference to muster support for the tax credits for synthetic fuels, solar and hydroelectric power, sponsored by Sens. Bob Packwood (R-Ore.) and Gaylord Nelson (D-Wis.), was joined by several trade groups and other organizations.

The groups are backing provisions that would cost about $14 billion of the tax bill's revenues over the 1980-1990 period. The coalition ranges from the American Gas Association to the Sheet Metal Workers' Association.