Former Senate majority leader Howard H. Baker Jr. (R-Tenn.) has chosen Thomas Rath, former attorney general of New Hampshire, to run his 1988 presidential campaign. Rath currently is managing the reelection campaign of Sen. Warren B. Rudman (R-N.H.), who was a close ally of Baker in the Senate. Rath said he expects Baker to announce his candidacy about a year from now. Baker won 13 percent of the vote in the 1980 Republican presidential primary in New Hampshire. He decided not to seek reelection to the Senate in 1984 so he could concentrate on his presidential campaign. According to the latest Washington Post-ABC poll, Baker is the choice of 12 percent of Republicans.

Rep. Harry M. Reid (D-Nev.) announced his candidacy for the Democratic nomination for the Senate seat held by Paul Laxalt (R-Nev.), who is retiring. A two-termer, Reid lost to Laxalt in 1974 by about 630 votes and will run this year against former representative James Santini, who switched to the Republican Party to make the bid.

Although Reid leads in two statewide polls by five percentage points, with many voters still undecided, his prospects are clouded by the gains Nevada Republicans have made in voter registration. Twenty years ago, the Democrats held a more than 2-to-1 majority in the state, but voter figures compiled last week show them leading by 153,141 to 129,087, a margin of 24,000. In the 1984, the Democrats' advantage was 37,000 registrants.

Massachusetts Republicans have had trouble finding candidates to challenge Democratic Gov. Michael S. Dukakis. Enter Gregory S. Hyatt, a lawyer who was a leader in the 1980 referendum campaign for Propsition 2 1/2, which cut taxes in the state, and who is leading the charge for the repeal of the state's mandatory seat-belt law. Hyatt told The Boston Globe that his campaign would focus on "the arrogance of power" in the Dukakis administration. He called the governor "an arrogant technocrat who's trying to tell us what to do." He gave Dukakis no credit for the state's healthy economy: "A robot or a mannequin could have managed this state's economy over the last four years."

Hyatt conceded that Dukakis will be "tough" to beat because "he's got a big machine. He's a machine politician."