Reference for Avodah Zarah 84:6
דיקא נמי דקתני גבי הקדש לא נהנין ולא מועלין אי אמרת בשלמא דאייתי עצים מעלמא היינו דקתני גבי הקדש לא נהנין ולא מועלין לא נהנין מדרבנן ולא מועלין מדאורייתא דהא לא קדישי
This conclusion is proved to be correct by the fact that when it came to a tree dedicated to the Temple it is stated: One may not make use of it, but if one does make use of it, it does not count as trespass. It makes sense if you say that [the bird] brought twigs from other places, for that is why it teaches with regard to a dedicated tree: One may not make use of it, but if one does make use of it, it does not count as trespass. “One may not make use of it” according to rabbinical law, “but if one does make use of it, it does not count as trespass,” according to the law of the Torah because [the twigs] were not dedicated.