The leading White House choice to fill a soon-to-be-vacant seat on the Nuclear Regulatory Commission is a black Republican engineer from Wisconsin, who congressional sources say is the subject of a conflict-of-interest charge filed in the Wisconsin legislature.

The charge against Willie J. Nunnery, 33, a member of the Wisconsin Public Service Commission since April, 1980, involves work he did for the District of Columbia Public Service Commission.

Wisconsin state Sen. Joe Strohl, a Democrat, asked the Wisconsin attorney general to investigate Nunnery's work in Washington as a hearing board examiner, charging that such outside employment is illegal under Wisconsin law.

Nunnery's name has been circulated during the last few weeks by White House aides on Capitol Hill as a probable NRC nominee, according to congressional sources. Nunnery would replace Commissioner Peter Bradford, who is leaving this spring to become a public advocate in the cabinet of the governor of Maine.

Strohl said Nunnery apparently violated state law requiring regulatory commissioners to "devote their entire time to their duties."

The law, Nunnery said, is "very vague and ambiguous," but he said he had complied with it and that he did most of the work in question at home in his spare time.

Lloyd Moore, general counsel of the District of Columbia PSC, said Nunnery was hired on a contract basis and had conducted one 90-minute hearing in September on the kinds of rules the commission should draw up on small power producers.

He said Nunnery received $90 per hour for actual hearing time and $75 per hour for time spent in preparing the case. Strohl said he had confirmed that Nunnery has received $5,946 so far and has billed the Washington PSC for another $1,300. He earns $46,700 a year from his Wisconsin post, Strohl said.

Strohl described Nunnery as "quiet, very low key . . . very pro-nuclear and not consumer-oriented." He said Nunnery's potential nomination had become controversial when Nunnery said criticism of his heavy reliance on staff work was racially motivated.