George Washington University officials have begun steps that could lead to dismissal of tenured professor Paul Arthur Crafton, who has been charged in Pennsylvania in connection with employment under different names at two state colleges there.

Federal authorities said yesterday that they have begun a formal investigation of Crafton's activities. Barbara Kosik of the U.S. attorney's office in Harrisburg, said the federal investigation--which could include inquiry into whether violations of laws covering passports, use of Social Security numbers or Internal Revenue Service regulations occurred--is being coordinated with the Pennsylvania attorney general's office's wide-ranging investigation.

Marianne Phelps, assistant university provost, said that an informal letter stating the university's concerns, the first of several steps in the formal termination procedure set by the faculty code, was sent to Crafton late last week. She would not discuss the letter's contents.

A.J.D. Schmidt, Crafton's attorney here, said yesterday he had not seen the letter and therefore would not comment on it. Although no time was set for Crafton to reply, Phelps said, "We would certainly hope to have this thing clarified by the end of this month."

If the letter does not prompt a solution satisfactory to the university, other officials said, the university could then take the more formal steps that could lead to a hearing before the Grievance Committee of the Faculty Senate and possible dismissal by the president and board of trustees.

Crafton has taught in the university's Engineering Administration Department since 1956, and has been a full professor there since 1960.