According to traditional Jewish law, a person is considered to be Jewish if his or her mother is Jewish. However, the Reform Movement declared, through a resolution of the Central Conference of American Rabbis passed in 1983:
“The Central Conference of American Rabbis declares that the child of one Jewish parent is under the presumption of Jewish descent. This presumption of the Jewish status of the offspring of any mixed marriage is to be established through appropriate and timely public and formal acts of identification with the Jewish faith and people. The performance of these mitzvot serves to commit those who participate in them, both parent and child, to Jewish life.
Depending on circumstances,mitzvot leading toward a positive and exclusive Jewish identity will include entry into the covenant, acquisition of a Hebrew name, Torah study, Bar/Bat Mitzvah, and Kabbalat Torah (Confirmation).For those beyond childhood claiming Jewish identity, other public acts or declarations may be added or substituted after consultation with their rabbi.”
In other words, parentage, whether the mother or the father, is a necessary, but not a sufficient, requirement for that person to be considered Jewish. In addition to having at least one Jewish parent, the person must also demonstrate that he or she identifies positively and exclusively as a Jew. Such a demonstration could be through adherence to the mitzvoth, through affiliation and attendance at a synagogue, through participation in Jewish education, or a variety of other ways.
The situation outlined in the question is somewhat more complicated. As far as I can determine from the way the question is worded, the situation is one of a person whose paternal (as it seems) grandparents were Jewish, but whose mother is not Jewish and whose father does not self- identify as Jewish. It can be assumed, therefore, that the questioner was not raised in a Jewish home, with Jewish education or Jewish practices.
When the Reform Movement passed its resolution on patrilineal descent, its Responsa Committee was asked a question which sheds some light on this situation. The question and answer are below:
“Contemporary American Reform Responsa
39. Patrilineal Descent and a Questionable Background*
QUESTION: A young man who grew up in England was a child of a mixed marriage and now wishes to marry an American Jewish girl. His father was Jewish and his mother was Anglican; both are deceased. The father was affiliated with the United Synagogue and the youngster believes he was ritually circumcised (berit milah) and named in the synagogue, although no formal record of this exists. He has had virtually no Jewish education. What is his status as far as we are concerned? We should note that the couple intends to settle in England. (A. D., New York, NY)
ANSWER: We base our decision on the resolution of the Central Conference of American Rabbis, March, 1983, and the responsum "Patrilineal and Matrilineal Descent." The Resolution reads:
"The Central Conference of American Rabbis declares that the child of one Jewish parent is under the presumption of Jewish descent. This presumption of the Jewish status of the offspring of any mixed marriage is to be established through appropriate and timely public and formal acts of identification with the Jewish faith and people. The performance of these mitzvot serves to commit those who participate in them, both parents and child, to Jewish life.
"Depending on circumstances, mitzvot leading toward a positive and exclusive Jewish identity will include entry into the covenant, acquisition of a Hebrew name, Torah study, Bar/Bat Mitzvah, and Kabbalat Torah (Confirmation). For those beyond childhood claiming Jewish identity, other public acts or declarations may be added or substituted after consultation with their rabbi."
As this young man can produce no evidence that he was ritually circumcised and named in the synagogue, and as he has had no Jewish education nor been involved in any subsequent acts which would affirm his Jewish identity, we would require conversion on the part of this young man as the affirmative way of establishing his Jewish identity.
October 1983”
In the Responsum question, the person was the child of an identifiably Jewish father. And yet his status as a Jew was rejected by the Responsa Committee, because he himself had taken no positive, affirmative steps in his life to demonstrate a Jewish identity. In the case of our questioner, neither parent is identifiably Jewish, nor can we determine if he or she has taken any steps to identify as a Jew. Therefore, the Reform Movement would not consider this person to be a Jew. If he or she wishes to identify as a Jew, a formal process of study and conversion must be undergone.