The Taiwan government has given away its Washington embassy and chancery-properties worth millions of dollars on the open market-in an apparent attempt to keep the Peking regime from claiming them after it is officially recognized as the sole government of China on Jan. 1.

The embassy, a historic residence at 3225 Woodley Rd. NW known as Twin Oaks, and the chancery offices at2311 Massachusetts Ave. NW were deeded to an American nonprofit corporation called Friends of Free China on Dec. 22, a week after President Carter announced the decision to recognize mainland China.

The total cost to the American group was $20- $10 for each property-according to the deeds, on file in the District of Columbia. The price was described by on attorney as a formality. The deeds were signed by Ambassador James C. H. Shen of the Republic of China (Taiwan).

Another deed, signed by Gen. Hahsiung Wen, director of the Chinese Government Procurement and Services Mission, sold the mission's property at 2224 R. St. NW to the America-Republic of China (AMROC) International Corporation for $193,000. A Taiwan embassy spokesman said yesterday that AMROC is a trading firm located in Washington and New York.

Friends of Free China, a nonprofit group incorporated in New York, has been in existence since 1973, according to the group's attorney, Brian P. Murphy. It is nonpartisan and has not enaged in lobbying activities, Murphy said, but tries to promote good will and cultural exchange between the United States and Taiwan.

The executive director of Friends of Free China is Jack E. Butram, a former aide to both Sen. Strom Thurmond (R-S.C.) and former Sen. Paul Fannin (R-Ariz.) during the 1960s. Butram, who lives in Greenville, S.C, could not be reached for comment.

State Department officials expressed some confusion yesterday about what the legal and diplomatic consequences of the gifts would be.

After France severed ties with Taiwan in the early 1960s, these officials said, the Taiwan embassy in Paris was taken away and given to the Peking government. The officials said they believed the action of the Taiwanese here probably was an effort to prevent a similar thing from happening in the United States.

Assistant Secretary of State Richard Holbrooke said yesterday that the department is "examining the legal ramifications" of the situation. Several officials said they believed the case would be litigated, but when and by whom was unclear. "It's up to the Peoples Republic (Mainland China)," one officials said.

"The question is, did they have the authority to transfer the properties after the president's announcement? Was it a fraudulent transfer?" said another State Department official involved in the case. "This will probably go to court and I'm reluctant to give anyone ammunition so I don't want to say any more."

There was some speculation that the gifts were made as an effort to keep the buildings for Taiwan's unofficial use after its official ties with the United States are broken. According to a member of the State Department's China Task Force, such nondiplomatic arrangements to facilitate trade and the issuance of visas have been made through essentially corporate bodies in several countries that have severed ties with Taiwan's government.

Taiwan's embassy officials declined to comment on the transaction. one . source close to the deal said that Friends of Free China received the properties with no strings attached and that everything had happened so suddenly that at this point it has made no plans about what to do with them.

The precise value of the buildings and land is difficult to determine since they have not been assessed for tax purposes since they were bought by the Nationalist Chinese.

The embassy which once belonged to the family of Alexander Graham Bell, inventor of the telephone, sits on 18 acres. When it was sold to the Chinese in the late 1940s the price was close to $425,000.Tregaron, the neighboring estate of the late ambassador to Moscow, Joseph E. Davies, is currently for sale at a price of $3.7 million.

There was some speculation yesterday that the hasty gift of the embassy was precipitated by Peking's attempts to buy Tregaron, perhaps with the intention of combining the two properties, but Tregaron's trustees said yesterday that they had not received any such proposals.