Just to clarify, the original comment was made by me in error and subsequently amended in the follow up comment to refer to Nativity scene and not the Christmas tree (the former being a religious symbol).
As such, the answer to your question is "it depends". Different courts in USA decided differently:
In some cases, it is permitted alongside other religious symbols:
In 2006, a lawsuit by the Alliance Defense Fund, a conservative Christian group in the United States, was brought against the state of Washington when it permitted a public display of a holiday tree and a menorah but not a nativity scene. Because of the lawsuit, the decision was made to permit a nativity scene to be displayed in the rotunda of the state Capitol, in Olympia, as long as other symbols of the season were included
But sometimes, Nativity scene is prohibited even if other religious symbols are included (src):
In federal court pleadings in the United States, for example, the New York City, school system defended its ban on nativity scenes by claiming the historicity of the birth of Jesus was not fact. The judge in the case upheld the ban, noting that the ban on nativity scenes is not discriminatory while permitting Jewish menorahs and Islamic star and crescent displays because the latter two have secular components while nativity scenes are supposed to be purely religious. In another instance, a suburban Philadelphia, Pennsylvania, school banned a nativity scene while permitting a menorah display. The school's principal stated, "Judaism is not just a religion, it's a culture"
On a personal level, I consider the last argument as pure hogwash of monumental proportions. Menorah (more technically, chanukkiyah, which is a special 9-branch Menorah displayed on Chanukkah and is usually involved in cases around Christmas) is mainly used to commemorate a divine miracle of the oil in one lamp lasting for 8 days, not exactly a secular idea.
