Federal officials have concluded after preliminary investigation that, despite some coincidental links, there was never a connection between John W. Hinckley Jr., who is charged with shooting President Reagan last week, and Edward M. Richardson, arrested Tuesday for threatening to "bring completion to Hinckley's reality."

H. Stuart Knight, director of the Secret Service, told a House subcommittee yesterday that "at this point in our investigation, we feel quite confident that there is no connection between the gentleman who was arrested and the events that went down last Monday."

Secret Service officials have reported an upsurge in threats against the president since he was shot March 30 and say this is a common phenomenon after a highly publicized assassination attempt.

The service and federal prosecutors in New York say Richardson, 22, of Drexel Hill, Pa., who was arrested by Manhattan's Port Authority bus terminal with a loaded revolver, apparently was trying to emulate Hinckley.

Authorities said Richardson had left threatening letters in a hotel room in New Haven, Conn., and like Hinckley, apparently was drawn to New Haven to gaze at actress Jodie Foster, a freshman at Yale University there. Like Hinckley, Richardson had spent some time recently in Lakewood, Colo., a Denver suburb.

New Haven police said yesterday that Richardson attended two performances of a student play in which Foster was appearing last weekend. She was under police guard at the time.

One of the letters found in Richardson's room at the New Haven hotel and released by authorities said: "I depart now for Washington, D.C., to bring completion to Hinckley's reality."

Richardson was reported as having told police that Hinckley appeared to him in a dream and told him to kill the president.

In Philadelphia, meanwhile, the Secret Service arrested a boarding-school employe on a charge of threatening Reagan's life, U.S. Attorney Peter A. Vaira said.

Steven A. Seach was arrested Monday, the day before Richardson was charged in New York City. According to Vaira, after Reagan was wounded March 30 Seach allegedly told a co-worker that "if he had been in Washington he would not have missed" and said he wanted time off to go to the capital and "finish the job."

Seach was arraigned before a U.S. magistrate and ordered to undergo a 90-day mental examination, Vaira said.

As various government agencies continue to investigate the shooting of Reagan, John Simpson, an acting assistant secretary at the Treasury Department which has jurisdiction over the Secret Service, said yesterday that "there is still every indication that the Secret Service performed superlatively."

Knight also reiterated in House testimony yesterday that a notebook left by a Secret Service agent in a public phone booth in suburban Virginia last weekend contained nothing that could compromise presidential security.

Several members of Congress have discussed various legislative responses to the assassination attempt. Yesterday, Senate Judiciary Committee Chairman Strom Thurmond (R-S.C.), whose seniority lends his bills considerable force, introduced legislation to establish mandatory prison terms any time a gun is used in a federal crime.

Thurmond's bill also would make it a federal offense to kill, kidnap or assault a Cabinet member, although statutory language already outlaws assault on any federal officer.

Thurmond's proposal also would set up procedures for imposing the death penalty for first-degree murder in the District of Columbia. The city's murder in the District of Columbia. The city's present maximum sentence is life imprisonment.

Thurmond did not propose to ban import of parts for small handguns, a prohibition that had stirred opposition from some gun owners' groups.