  CeRh$_2$As$_2$ is an unconventional superconductor with multiple
superconducting phases and $T_\mathrm{c} = 0.26$ K. When $H\parallel c$, it
shows a field-induced transition at $\mu_0H^* = 4$ T from a low-field
superconducting state SC1 to a high-field state SC2 with a large critical field
of $\mu_0H_\mathrm{c2} = 14$ T. In contrast, for $H\perp c$, only the SC1 with
$\mu_0H_\mathrm{c2} = 2$ T is observed. A simple model based on the crystal
symmetry was able to reproduce the phase-diagrams and their anisotropy,
identifying SC1 and SC2 with even and odd parity superconducting states,
respectively. However, additional orders were observed in the normal state
which might have an influence on the change of the superconducting state at
$H^*$. Here, we present a comprehensive study of the angle dependence of the
upper critical fields using magnetic ac-susceptibility, specific heat and
torque on single crystals of CeRh$_2$As$_2$. The experiments show that the
state SC2 is strongly suppressed when rotating the magnetic field away from the
$c$ axis and it disappears for an angle of 35$^{\circ}$. This behavior agrees
perfectly with our extended model of a pseudospin triplet state with $\vec{d}$
vector in the plane and hence allows to nail down that SC2 is indeed the
suggested odd-parity state.
