From Wikipedia:
"On December 21, 1995, Bethlehem became one of the areas under the full control of the Palestinian Authority. It is capital of the Bethlehem district. The current population of the town is about 40,000. The Christian population is no longer the majority, but a special statute requires that the mayor and a majority of the municipal council must nevertheless be Christian".
Of course that was ten years ago but I suspect that Palestinians would say it is in Palestine and Israelis might say it is in Israel.