Its strong form does not hold in Brans-Dicke theory, and its weak form is joined by local position invariance and local Lorentz invariance in the version named for the man who popularized it.  
Lunar laser-ranging observations limit the strength of the Nordtvedt effect, which would violate the strong form of this statement.  Its strong form does not hold in Brans-Dicke theory, and its weak form is joined by local position invariance and local Lorentz invariance in the version named for the man who popularized it.  It was tested by the torsion balance experiments of Eötvös and the Pound-Rebka measurement of gravitational redshift, a phenomenon predicted by this statement.  A thought experiment of a free-falling elevator was used by Einstein to illustrate, FTP, this axiom of general relativity whose weak form states that inertial and gravitational mass are the same.
Lunar laser-ranging observations limit the strength of the Nordtvedt effect, which would violate the strong form of this statement.  
{equivalence} principle