  1T-TaS$_2$ undergoes successive phase transitions upon cooling and eventually
enters an insulating state of mysterious origin. Some consider this state to be
a band insulator with interlayer stacking order, yet others attribute it to
Mott physics that support a quantum spin liquid state.Here, we determine the
electronic and structural properties of 1T-TaS$_2$ using angle-resolved
photoemission spectroscopy and X-Ray diffraction. At low temperatures, the
2$\pi$/2c-periodic band dispersion, along with half-integer-indexed diffraction
peaks along the c axis, unambiguously indicates that the ground state of
1T-TaS$_2$ is a band insulator with interlayer dimerization. Upon heating,
however, the system undergoes a transition into a Mott insulating state, which
only exists in a narrow temperature window. Our results refute the idea of
searching for quantum magnetism in 1T-TaS$_2$ only at low temperatures, and
highlight the competition between on-site Coulomb repulsion and interlayer
hopping as a crucial aspect for understanding the material's electronic
properties.
