A 10-month investigation by the Treasury Department has found no support for charges made last summer that Mobil Oil Corp. supplied Rhodesia's white-minorty government with petroleum products in violation of a ban on trading with the African country.

The United Church of Christ's Office for Church in Society (previously called the Center for Social Action) alleged the Mobil trade with Rhodesia when it released copies of purported Mobil internal documents relating to petroleum product shipments.

United Church officials displayed the copies of letters, invoices and accounting sheets at a widely covered Washington news conference called by the Peoples Bicentennail Commission, as small activist group that converted the Constitution.

The Treasury Department's Office of Foreign Assets Control concluded that if the documents were authentic, "They would constitue convincing evidence of the truth of the allegations that Mobil South Africa was supplying Mobil Rhodesia through several intermediary sources."

However, the government agency said overall authenticity could not be established. While Secret Service handwriting analysis or confirmation by Mobil showed two documents were valid copies, "the possible interference that all the documents are authentic is substantially weakened by the fact that one of the two . . . is not on its face incriminating" while the other was signed by a low-level Mobil South Africa employee, the agency said.

The main barrier faced by Treasury investigators in studying the allegations was the refusal of Mobil's subsidiary in South Africa to provide documents or testimony requested - either to the U.S. government or to the giant, New York - based petroleum firm itself.

Mobil officers and Treasury officials sought information from the South African company but were told bluntly that an "official secrets act" prohibited dissemination of such information. "If fact . . . (Mobil officers who went to South Africa from New York) were themselves advised that they wiuld place their attempted to conduct any investigation into the matter," the Treasury said.

Treasury investigators did study all documents in the hands of Mobil officials in this country, including data on production and consumption of international subsidiary products. They found no discrepancy that would suggest diversion of Mobil products to Rhodesia and concluded there "is a genuine possibility" that petroleum products in Rhodesia all originated with South Africa's Coal Oil and Gas Corp.(SASOL).

A spokeswoman for the United Church center said it had not yet recieved a copy of the Treasury investigation and witheld comment until the report is studied.