South Dakota, home of the giant carved heads of presidents on Mt. Rushmore, is currently involved in a furor over the arrival of a new, considerably more abstract sculpture by California artist Guy Dill.

In fact, 5,000 of the 14,000 inhabitants of Huron S.D., birthplace of the late Hubert Humphrey, have signed a petition asking the General Services Administration to remove the 45-foot-long, black steel-and-wood sculpture recently placed in front of the new federal building there. The sculpture, entitled "Hoe-Down," was commissioned by the GSA from Dill for $25,000.

The protest was revealed at congressional hearings yesterday before the Governmental Affairs Subcommittee on Civil Service and General Services by new GSA head, former Rear Adm. Rowland G. Freeman III. Joan Mondale, former GSA head Jay Solomon and sculptor George Segal also spoke on behalf of the GSA's Art-in-Architecture program, of which the Dill commission was a part.

Dill, who is head of the sculpture department at UCLA and has works in the Museum of Modern Art, the Whitney and Guggenheim museums, said last night that he found the whole situation "unsettling." "I expected some dissension, but not of this magnitude. I put my soul into the work and I'll stand by it. My feeling is that this has more to do with government programs and inflation and fuel prices than with me personally."

He may be right. According to Roger Kasa, managing editor of the Huron Daily Plainsman, "The people began by objecting to the fact that they had no say in what went up here. But it got to be a grass-roots rebellion against government waste. We have taken an editorial position supporting the committee to get rid of it and change the procedure now being used to select artists." The committee is headed by Clifford Roth, a local plumber, who presented the petition to Rep. Abdnor (R-S.D.) at the state fair earlier this month.