Senate Majority Leader Robert J. Dole (R-Kan.) yesterday named Sheila P. Burke as his new chief of staff, making her the highest-ranking woman in the Senate leadership hierarchy -- one of the few women, in fact, to hold a high staff position in the Senate as a whole. Senate watchers say that, as deputy chief of Dole's staff, she was the obvious choice to replace Roderick DeArment, who resigned to become a partner in the Washington law firm of Covington and Burling.

Burke is a trained nurse with a graduate degree in public administration from Harvard University. After joining the Senate Finance Committee staff in 1979, she became deputy staff director under Dole in 1982, and moved to the majority leader's office when Dole was elected to that post last year.

Like Dole, Burke has a high-powered, dual-Washington-insider-career marriage -- to David Chew, a top aide to White House chief of staff Donald T. Regan.

Watching the Watchdog's Watchdog . . . Sharon Connelly, head of the Nuclear Regulatory Commission's Office of Inspector and Auditor, has been placed on "administrative leave," with pay, while the NRC and a congressional subcommittee investigate her office's handling of a sexual harrassment complaint. At issue is whether Connelly bungled the handling of a complaint against her deputy, George Messenger. It is said on the Hill that she not only tried to discourage the female complainant from filing against Messenger, but that she may have gone so far as to threaten reprisals against the employe. A third member of the staff, special assistant George A. Mulley, is said to have combed the personnel files -- which contain the cullings of security clearance investigations -- of the victim and three other people who testified on her behalf.

Rep. Edward J. Markey's (D-Mass.) subcommittee on Energy Conservation and Power is the group that prodded the NRC into action. .

Rhetoric 101 . . . Another concern of Markey's subcommittee is what effect Gramm-Rudman-Hollings cuts are apt to have on the Energy Department's budgets for environmental cleanup and protection of nuclear installations from terrorism. In discussing the issue early this week, Markey made the following contribution to public discourse: "Grambo is swinging its machete through ongoing efforts to clean up DOE's polluted nuclear-industrial swamp, but the White House has ordered its technocrats to protect the X-ray laser and other crown jewels in the nuclear temple of doom." This was apparently a prepared statement.