If Muriel Humphrey really wants her state party's endorsement for election to the Senate in November, she'll have to start lining up support at the precinct level within the next few weeks.

Under the Minnesota Democratic Farmer-Labor Party's system, the endorsement process begins in 4,000 precincts Feb. 28. Precinct meetings elect delegates to the march county conventions, which, in turn, pick delegates to the endorsing June state convention. A 60 per cent majority is needed for endorsement.

Humphrey, who was appointed Wednesday to the senatorial seat of her husband, Hubert, by Gov. Rudy Perpich, has left open the possibility of running in November's election to fill the remaining four years of the term, although Minnesota politicians generally expected that she would serve only as a caretaker.

The convention rules do not require a candidate declare formally for an office, and support could be generaged among uncommitted as well as committed delegates. But as a practical matter Humphrey faces that fact that there is a major candidate in the field already - Rep. Donald Fraser, a leader in the Democratic Farmer-Labor Party's liberal wing.

Supporters of Fraser, who announced his candidacy on Monday, two days before the appointment, conceded yesterday it would be difficult to campaign against the late and revered senator's silent political partner. Ironically Hubert H. Humphrey, in light of his failing health due to inoperable cancer, had encouraged Fraser to consider running.

Mrs. Humphrey, who is expected to remain on vacation in the Virgin Islands until Feb. 8, has no Minnesota political plans yet, according to the Minneapolis Humphrey office.

Minnesota Republicans, caught off guard even more than their Democratic counterparts by the open Humphrey options, loosed a bitter barrage on Perpich, who also appointed Wendell Anderson to the Senate 13 months ago to succeed Vice President Mondale. At the time, Anderson was governor, Perpich lieutenant governor.

Rep. Tom Hagersorn (R), a possible Senate candidate himself, said, "It's almost a shambles - two non-elected senators, both appointed by a non elected Gov. Perpich, and a non-elected lieutenant governor."

Also, Rep. Bill Frenzel (R), from a suburban Minneapolis district, said, "this will cost Gov. Perpich's job. I think the people ought to run the governor out of the state." Frenzel contended perich "double-crossed the people" by not naming a caretaker senator.

Frenzel had been considering a quest for Humphrey's senate seat, but is reconsidering. The eldest Humphrey son, state Sen. Hubert H. Humphrey III, is seeking the Democratic Farmer-Labor Party endorsement forthe House in Frenzel's district.