Questions around conversion and Jewish identity present a number of complex issues and there are a variety of factors that can come into play in any given situation. In any case like this, I would urge you to consult with your rabbi. In the Conservative Movement, the rabbi of a synagogue sets the policies and practices for their particular community (mara d'atra).
As the question is presented, my presumption is that we are talking about a case of a Jewish woman who perhaps married someone who is Christian and the couple raised their child as a Christian. Let's say the child grows up and now, as an adult, rejects Christianity and wishes to reconnect with their Jewish roots. The question then is: how can this person, who was perhaps baptized and socialized in Christianity, now rejoin the Jewish people and practice the religion of Judaism?
According to Jewish law (halacha), a person born to a Jewish mother is Jewish, even if they do not practice Judaism. However, the question of someone who leaves Judaism to practice another religion poses some difficulties and raises doubts.
There is a principle that derives from the Talmud which states: "A Jew, even if he/she sins, is still considered a Jew." (see. BT Yevamot 47b, B'horot 30b, Sanhedrin 44a). The medieval commentator Rashi (11th C. France) interpreted this statement to mean that an apostate Jew who wishes to return should be treated with leniency and welcomed back without conversion. However, some scholars have noted that in Rashi's time, and for most of Jewish history, Jews who left the faith were most often coerced or pressured to convert. That is not the case today. Adults who leave Judaism and practice another religion do so by choice. These individuals should be treated as apostates and, according to the Conservative Movement, if they wish to return must undergo a formal affirmation of their Jewish identity through the ritual of immersion in the mikvah (t'vilah) and circumcision for males. (see J. Roth & A. Lubow, "Standard of Rabbinic Practice Regarding Determination of Jewish Identity" in The Proceedings of the Committee on Jewish Law and Standards, 80-85. p 178).
With the case of a child raised in another religion, an additional legal principle may be considered. The Talmud discusses the possibility that a child who was taken captive by gentiles and raised in another religion would not be liable for violations of Shabbat (BT Shabbat 67b-68b). From this idea, we might also take a lenient approach to a child raised as a Christian who wishes to be recognized as Jewish.
Based on our discussion thus far, it would be reasonable to conclude that the Torah ("d'oraita") does not strictly require conversion to Judaism in our case of a child raised in another religion. The only caveat would be that a male in this situation who was not circumcised would require brit milah, and if previously circumcised would require hatafat dam brit.
However, all this being said, as a practical matter Jewish rabbinic tradition ("d'rabbanan") dictates that we have to go beyond the narrow letter of the law and consider the very real emotional and social needs of the individual and community. A person who was raised as a Christian, perhaps baptized and educated in the church, and wishes to be recognized as Jewish has a need to be socialized into the Jewish community and learn how to practice the religion of their ancestors. This person should find a synagogue to which they want to belong and a rabbi to guide them in their integration into the community. It would be appropriate for them to undertake a course of study, like a conversion or "introduction to Judaism" class.
But, study and socialization are not quite enough. Ritual is how human beings mark moments of transition and meaning in life, imbuing them with holiness and intention. In order for this individual to be affirmed in their Jewish identity and in order for the community to be left with no doubts about this person's sincerity, a formal ritual is necessary. When the individual is ready, the rabbi should convene a beit din (rabbinic court) and bring this person to the mikvah for a ritual immersion (and if male, the person also needs brit milah or hatafat dam brit). Mikvah is a powerful ritual of rebirth. From the womb-like water of the mikvah the person who was raised as a Christian emerges renewed and affirmed in their Jewish identity. Only through such a ritual can this person be assured that their Jewish status will not be questioned.