One question in the Caddell poll indicated that Mr. Springer had been arrested on a morals charge with three women in a motel room; that he had used a bad check to pay for their services, and then later resigned as Mayor.

Mr. Springer says that he was not arrested, that there were not three women in the room, and that the check did not bounce. He added that he was not Mayor at the time of the incident.

''Perhaps, like you, I'm not sure what any of this has to do with being Governor,'' he says in the television commercial. ''But maybe my talking to you about this makes a point. Ohio is in a world of hurt. The next Governor is going to have to take some heavy risks and face some hard truths. I'm prepared to do that.

''This commercial should be proof. I'm not afraid, even of the truth, and even if it hurts.'' After the 1974 incident, at a health club in Fort Mitchell, Ky., Mr. Springer resigned from the Cincinnati City Council. Since then, he has told audiences how he held his marriage together and made a political comeback, gaining re-election to the council in 1975 and later serving as Mayor.

''Honesty is the best policy,'' said Michael Ford, his campaign manager. The poll was taken by Mr. Caddell's Cambridge Survey Research, the company used by Jimmy Carter in his 1976 and 1980 Presidential campaigns. Mr. Caddell said the question and its results ''were never meant for public consumption'' and that he took ''responsibility for any innaccurate information.''