She is an MD, but NOT a licensed MD and therefore can not practice medicine in CT. However, it appears that she is.
According to the Yale website for her, she is accepting patients.
In addition, her publications and statements concerning Trump are considered medical diagnosis since she is a psychiatrist and making statements concerning his mental status. That is considered practicing medicine.
The Goldwater rule is the informal name given to Section 7 in the American Psychiatric Association’s (APA) Principles of Medical Ethics that states it is unethical for psychiatrists to give a professional opinion about public figures they have not examined[further explanation needed] in person, and from whom they have not obtained consent to discuss their mental health in public statements. It is named after presidential candidate Barry Goldwater.
The issue arose in 1964 when Fact published the article “The Unconscious of a Conservative: A Special Issue on the Mind of Barry Goldwater”. The magazine polled psychiatrists about U.S. Senator Barry Goldwater and whether he was fit to be president. The editor, Ralph Ginzburg, was sued for libel in Goldwater v. Ginzburg where Goldwater won $75,000 (approximately $592,000 today) in damages.
Section 7, which appeared in the first edition of the APA’s Principles of Medical Ethics in 1973 and is still in effect as of 2017, says:
On occasion psychiatrists are asked for an opinion about an individual who is in the light of public attention or who has disclosed information about himself/herself through public media.
In such circumstances, a psychiatrist may share with the public his or her expertise about psychiatric issues in general. However, it is unethical for a psychiatrist to offer a professional opinion unless he or she has conducted an examination and has been granted proper authorization for such a statement.