After looking at the governor's race and the Senate race, Rhode Island Lt. Gov. Richard Licht (pronounced leach), a Democrat, has set his sights on Washington and will challenge Sen. John H. Chafee (R) next year. A poll taken last spring showed Chafee with 44 percent support and Licht 32 percent.

Chafee, first elected in 1976, won reelection in 1982 by fewer than 10,000 votes. His opponent tied him to President Reagan -- a strategy Licht may try. Although Chafee is obviously favored, Licht takes encouragement from a little personal history: In 1968, Chafee, seeking his fourth term as governor, was upset by Democratic challenger Frank Licht, Richard's uncle.

Meanwhile in Washington state, Sen. Daniel J. Evans (R), who was elected in 1983 to serve the remainder of the term of the late senator Henry M. Jackson (D), has raised only $20,000 this year, fueling speculation that he won't seek reelection.

But Evans' press secretary, Lee Keller Reis, said the low level of fund-raising "reflects Evans' view that campaigns last too long and cost too much." She said Evans has not decided what to do and plans to make an announcement in the fall.

Four House Democrats -- Reps. Al Swift, Don Bonker, Norman D. Dicks and Mike Lowry -- are looking at the Senate seat. But all but Swift have said they would be less inclined to run if Evans does.

Swift has said he will run "unless I see something negative, something unanticipated, like everyone hates me."

And finally, Rep. Robert T. Matsui (D-Calif.), weeks after announcing he was considering challenging Sen. Pete Wilson (R-Calif.), said he will not.

Matsui said he came to his decision after consulting former representative Ed Zschau (R-Calif.), who unsuccessfully challenged Sen. Alan Cranston (D-Calif.) last year. Matsui, acknowledging that he would have been an underdog, said he felt he could not give up his House responsibilities and "basically live in California. I just didn't feel I was able to give that kind of commitment . . . . "

Matsui's decision is expected to strengthen the position of Lt. Gov. Leo McCarthy (D), who has taken the early initiative. Secretary of State March Fong Eu is also in the Democratic race, and Los Angeles television commentator Bill Press is likely to join them.