Presidential assailant John W. Hinckley Jr. has requested an absentee ballot from Colorado, telling elections officials in that state that he would "very much like to vote" in the November election in which Ronald Reagan is a candidate.

Hinckley, 29, confined to St. Elizabeths mental hospital here since June 1982 for shooting Reagan, said in a two-paragraph, typewritten letter to the Denver election commission that a similar request to vote in the District of Columbia had been denied.

A jury found Hinckley innocent of the March 31, 1981, shooting of Reagan by reason of insanity. In an Aug. 17 letter, D.C. Registrar Joe Baxter rebuffed Hinckley's request to vote here, questioning both Hinckley's residency qualifications and his mental competency.

Persons ruled mentally incompetent are unqualified to vote under D.C. elections laws, elections board general counsel William H. Lewis said yesterday. Lewis said Hinckley could appeal Baxter's action to the elections board, but has not done so.

In Colorado, Norman Allen, the clerk and recorder of Jefferson County, the suburban jurisdiction where Hinckley's parents live, said yesterday that "at the moment, I don't see any reason why he couldn't be registered."

Allen said he intends to reply to Hinckley's request with a standard letter explaining the county's registration requirements. "If he can swear that he's 18 years of age and that he was a resident of the county at least 32 days before he went into the hospital, that should do it."

Testimony at Hinckley's trial in 1982 indicated that he wandered widely in the months before he shot Reagan, but used his parents' house in the Denver suburb of Evergreen, Colo., as an intermittent home.

Allen said that commitment to a mental hospital is not a bar to voting in Colorado. If Hinckley had been convicted of a crime he could not vote, Allen said. "But normally if you're absent in a hospital, you can be registered," he added.

If Hinckley completes the registration procedure by Oct. 5, he could get an absentee ballot for the Nov. 6 election, Allen said.

Hinckley last week asked a U.S. District Court judge here for expanded privileges, including more access to reporters and permission to walk the St. Elizabeths grounds, during his confinement. The judge, Barrington D. Parker, has not ruled on the request.