This paper develops sharp testable implications for Tobit and IV-Tobit models' identifying assumptions: linear index specification, (joint) normality of latent errors, and treatment (instrument) exogeneity and relevance. The new sharp testable equalities can detect all possible observable violations of the identifying conditions. We propose a testing procedure for the model's validity using existing inference methods for intersection bounds. Simulation results suggests proper size for large samples and that the test is powerful to detect large violation of the exogeneity assumption and violations in the error structure. Finally, we review and propose new alternative paths to partially identify the parameters of interest under less restrictive assumptions.