The relevant statute appears to be the 47 CFR 97.15 cited in the answer.
PART 97: AMATEUR RADIO SERVICE
Subpart A: General Provisions
97.15 - Station antenna structures.
(a) Owners of certain antenna structures more than 60.96 meters (200
feet) above ground level at the site or located near or at a public
use airport must notify the Federal Aviation Administration and
register with the Commission as required by part 17 of this chapter.
(b) Except as otherwise provided herein, a station antenna structure
may be erected at heights and dimensions sufficient to accommodate
amateur service communications. (State and local regulation of a
station antenna structure must not preclude amateur service
communications. Rather, it must reasonably accommodate such
communications and must constitute the minimum practicable regulation
to accomplish the state or local authority's legitimate purpose. See
PRB-1, 101 FCC 2d 952 (1985) for details.)