Hartford, Conn. — Like it or not, Vice-President George Bush soon may find himself immeshed in a political battle that could cost his party a US Senate seat. Mr. Bush appears determined to stay clear of efforts within the Connecticut GOP to deny a third term to maverick US Sen. Lowell P. Weicker Jr. But Bush's neutrality is complicated by the fact that he grew up in Connecticut and that the challenger for the senatorial nomination is his elder brother, Prescott Bush Jr.
The latter's declaration, expected in early January, is eagerly awaited by Republican conservatives in the state, many of whom consider Senator Weicker too liberal.
Particularly displeasing was his vote last winter against President Reagan's federal budget. Weicker was one of only two Republicans to vote against it.
For this reason there is a lot of enthusiasm among Reagan supporters here for a new senator, one they see as more in step with the White House on key policies.
The Bush family has been extremely popular on the Connecticut political scene for decades, especially among fellow Republicans. The late Prescott S. Bush Sr. was a US senator for Connecticut from 1952 to 1963. In early 1980, George Bush carried the state in its presidential primary.
The vice-president's brother, who is an insurance executive and resident of Greenwich, the home town of Senator Weicker, is viewed by Connecticut Republicans as a conservative, or at least more of a moderate than the incumbent.
Senator Weicker makes it clear he will run. If unsuccessful in a GOP renomination, he says he will run as an independent.
This would create a situation similar to that in 1970, when as the GOP nominee he bested the Democratic nominee and then Democratic US Sen. Thomas Dodd , whose party had denied him renomination following a Senate censure for misconduct in office.
Two candidates have surfaced on the Democratic side: fourth-term US Rep. Toby Moffett of the state's 6th congressional district and Atty. John T. Downey of New Haven, a former CIA agent who spent 20 years in a Chinese prison after his capture during the Korean War.
Mr. Moffett, a liberal who first gained state prominence in the early 1970s as a consumer advocate, has strong backing from within party ranks, including former Vice-President Walter Mondale and US Sen. Edward M. Kennedy (D) of Massachusetts.
Connecticut political observers, including activists in both major parties, generally anticipate Moffett will win the Senate nomination.
Meanwhile speculation abounds concerning a three-way ballot scramble for the Senate seat next November.
That Senator Weicker could have difficulty in recapturing the Republican nomination was indicated in a recent voter sampling conducted by the Institute of Social Inquiry at the University of Connecticut. It found that among GOP voters senatorial hopeful Bush led the GOP incumbent 44 percent to 33 percent.
But among all voters, figures are more encouraging from the Weicker standpoint. The poll showed him in a virtual tie with Democrat Moffett, 31 percent apiece, and Republican Bush trailing with 18 percent in a three-way contest.
Democrats outnumber Republicans 669,000 to 449,000 in Connecticut. The balance of political power, however, is held and often wielded by so-called independents - those registered but enrolled in neither party, who number 586, 000.
Among Democrats, the sampling indicates Weicker is more favored than Bush: Moffett was favored 42 percent to 34 percent for Senator Weicker and 10 percent for Bush.
In a similar three-way battle among Republican voters, Mr. Bush held a 40 percent to 27 percent edge over Mr. Weicker, with 15 percent favoring Democrat Moffett.
While cautioning that polls conducted a year before an election can present a somewhat distorted picture, Dr. Everett Ladd, who heads the inquiry institute, notes that ''ordinarily one might expect an incumbent senator to show greater strength within his party.''
In spite of the University of Connecticut figures, Republican conservatives hold that Bush prospects are bright, especially in a three-way election contest with Messrs. Weicker and Moffett since the latter candidates would tend to split the liberal vote.
Moffett in his Dec. 1 senatorial candidacy declaration described it as ''the best hope in the nation for Democrats to capture a seat in the Senate'' from the Republicans.
He questions how effective a job Mr. Weicker can do for Connecticut in the light of his disagreements with the Reagan administration that make him, Moffett says, ''a member of neither party.''