D.C. Corporation Counsel John R. Risher Jr. said yesterday that his office is conducting an "inquiry" into whether City Counsil Chairman Sterling Tucker should be removed from office for allegedly violating city laws restricting Tucker's outside income.

Risher's announcement follows disclosures last week that Tucker earned $7,084 last year as a lecturer and adviser to the Howard University School of Social Work. The city's home rule charter prohibits the Council chairman from holding any other job for which he is paid a salary.

Risher's announcement came in an atmosphere laden with political overtones, Tucker is considered a leading candidate for the Democratic mayoral nomination in 1978. Risher's boss, Mayor Walter E. Washington, is also believed to be contemplating running for mayor in 1978. Risher is one of the mayor's closest advisers.

In addition to Risher's inquiry, there was a heated debate Thursday night at the regular meeting of the D.C. Democratic State Committee over a resolution that would have urged the committee to request a probe of Tucker's actions by the U.S. Attorney's Office, the corporation counsel and the D.C. Board of Elections and Ethics.

That resolution, which eventually was tabled> was introduced by R. Calvin Lockridge, a member of the state committee who was elected on a state supported by Mayor Washington. Lockridge also has written a letter to the board of elections asking it to investigate Tucker. Lockridge, contending that he has no political or personal relations with the mayor, said yesterday that his actions were not politically motivated.

This week's action at the Democratic committee meeting marked the second time this year that an attempt has been made to embarrass Tucker within the ranks of the party's central committee.

In February, Council member Douglas E. Moore (D-at large) tried unsuccessfully to get the committee to censure Tucker for devising a Council reorganization plan that stripped fellow Democrat Moore of the chairmanship of the powerful budget committee.

Sources close to the mayor flatly denied that Washington was in any wasy personally involed in the efforts.But one mayoral confident conceded that "I can't argue that that if Sterling got kicked out, it wouldn't be good for the mayor."

Sources close to the Council chairman said yesterday that the efforts to carry out the investigations appear to be part of a campaign to embarrass Tucker through a series of damaging stories in the media.

The allegations of improper action, these sources note, stemmed from public financial statements filed by Tucker in which the outside income from lecturing at Howard, where Tucker has taught for 15 years, were clearly reported and identified.

Tucker has said that he consulted leaders of both the House and Senate District committees during the preparation of the home rule charter, and was assured at that time that his teaching duties were not included in the prohibition against outside employment that was eventually written into the home rule charter.

"The issue is obviously to get Tucket out of the way, either in the courts or in the media," one city political observer close to Tucker said yesterday.

Ever since the allegations concerning Tucker have appeared, persons close to the mayor have at times urged reporters to show more interest in the story.

At one point this week, Sam Eastman, the mayor's press secretary, called the The Washington Post and requested copies of previous newspaper articles concerning a $25,000 trust fund administered by Tucker on behalf of his children.

The U.S. Attorney's Office last summer investigated Tucker's involvement in the trust fund from the Taconic Foundation, but found no evidence of wrongdoings. Tucker never had direct access to the fund, and dissolved it on Oct. 13, 1976.

As part of the local investigation, Risher requested and obtained from the U.S. attorney's fraud division its file on the Tucker trust fund late this week, The Post learned. Risher reportedly indicated an urgency for the material, and sent a government messenger the 10 blocks between the District Building and the U.S. Courthouse to pick up the file.

The board of elections is expected to decide next week whether it will begin its own investigation.

Risher refused repeatedly yesterday to outlined the scope of his "inquiry," but asserted that his office had jurisdiction to begin proceedings in D.C. Superior Court that could lead to a jury trial in which Tucker's fate would be would be decided.

One District Building source said yesterday that Risher's efforts appear to be aimed at building enough pressure around Tucker to force his voluntary resignation. Were Tucker out of the race, prospects for the mayor's reelection in 1978, should he decide to run, would be improved considerably.

Risher said he was aware that some people might attach political overtones to his action. "I didn't come in to do the mayor's bidding," Risher said. "I came in to do the job that's required of the incumbent in this office."

Risher was appointed corporation counsel by the mayor a year ago. When Washington was elected in 1974, Risher was the general counsel of the Washington Election Committee. During that same campaign, Lockridge worked for the mayor's principal opponent, Clifford L. Alexander Jr.

Lockridge is one of only three persons from the Washington-backed Open Party slate elected to the central committee last year. The other 41 members were part of the Unity 76 Coalition, whose leaders included Tucker. Committee chairman Robert B. Washington Jr. is a strong Tucker supporter.

Lockridge, who said yesterday that he believes that Tucker has violated the law and should be removed from office, contended at the committe meeting that the party should not remain silent at a time when city Republicans were calling on the U.S. Attorney's Office for an investigation. CAPTION: Picture, STERLING TUCKER . . . $7,084 from Howard U.