A House-Senate conference committee resumed work yesterday on President Carter's proposed crude-oil tax, but failed to resolve the key issue of how to apportion the levy betwen major oil firms and independents.

In a day largely spent debating, the conferees were able to agree on only a few, essentially procedural issues -- narrowing their choices on what tax rate to impose on existing oil and several similar questions.

At the same time, panel members indicated they intended at least to explore seriously proposals to scrap part or all of the Carter tax and replace it with flat excise tax, which sponsors say would be simpler than Carter's plan.

There was no immediate indication how much support the substitute would muster when the committee meets again this morning. The plan has the backing of some independent producers, but panel members seemed mixed.

Although the panel failed to resolve the question of how heavily to tax the big oil firms compared to the independents, it was clear from the debate that the smaller firms will lose some of the breaks voted them by the Senate.

Panel members were toying yesterday with the notion of cutting breaks for independents to half the roughly $50 billion provided under the Senate version of the bill. The House bill makes no such provision.

If the committee does not vote to replace the Carter plan with a severance tax, it also most likely will move to use a single tax rate for oil produced before and after 1973, rather than splitting the rate as both measures do now.

The panel voted tentatively yesterday to set that overall rate at between 65 and 70 percent, compared to 75 percent in the House bill and 10 percent in the Senate's, and to impose the tax only on that portion of the price over $13 a barrel.

The crude-oil tax, which Carter originally labeled "Windfall profits tax," was designed to tap some of the extra monies the oil industry would receive as a result of higher oil prices, and divert it for public use.