The D.C. Court of Appeals ordered yesterday a full hearings into a Maryland woman's request that court files on her adoption by opened so she can learn the identify of her natural parents.

For the first time, the appellate court took note in a brief opinion of what it called "an increaseing well of support" for access to such records and said city courts now should "come to grips with this touching and recurring social question."

The woman, 21, married and the mother of two children, was adopted is the District of Columbia when she was 3 year old, according to the court record.

In June 1970 the woman, who is not identified in the court opinion, filed a petition in D.C. Superior Court asking that records of her adoption be made available to her. Under city law such records are sealed and can be inspected only when a court determine's that the welfare of the adopted person will be "promoted or protected."

In January, 1977 then Judge Charles W. Halleck denied the woman's-request without a hearing in Suuerior Count. Lawyers familiar with the case said Halleck's decision concentrated on possible adverse effects on the woman's natural parents if disclosure were made.

Acknowledging that at times there may be "social complications and risks to the adoptee and the natural parents" if records are opened, the appeals court said that is not enough to deny a hearing at the outset of a case.

The court said the case should be returned to Superior Court for a decision "after a searching exploration that will come from a full evidentiary hearing." The appeals court did not address the merits of the woman's request.

The appeals court opinion was written by Judge George R. Gallagher, with concurrence from Judge Jultz Cooper Mack and Superior Court Judge John D. Fauntleroy, who sat on the appellate panel by designation.

The oppeals court noted that the case involved an Milut adoptee and said the same request by a minor would pass different considerations."

Units opinion, the court said it would be "difficult to illegible" a more persuasive showing by an adoptee than was made in this case.

The court noted that in its opinion that the woman contends that because she does not know her natural parents, she is left, in her own words: with "an emptiness and confusion about who I am."

The opinion said the woman feels deprived of the love that could be shared with her natural family. She also cited a desire to know whether her natural family has any hereditary diseases, the court said.The woman's adoptive parents fully support her search, the court said in the opinion.

On appeal, the D.C. corporation counsel's office argued primarily that the records should remain closed because a natural parent relies on the secrecy of court records when a child is placed for adoption, Assistant Corporation Counsel Dennis McDaniel soid.

David Sadoff, an attorney who represents the woman, said the law does not provide for absolute secrecy of records, and he argued that the court must blance the adult adoptees' need for such information against the natural parent's right to privacy.