We construct crosscap states in the N = 2 Liouville theory from the modular
bootstrap method. We verify our results by comparing it with the calculation
from the minisuperspace approximation and by checking the consistency with the
conformal bootstrap equation. Various overlaps with other known branes are
studied. We further discuss the topological nature of the discrete terms in the
crosscap wavefunction and their connection with the Landau-Ginzburg approach in
a nontrivial dilaton background. We find that it can be mapped to the
Landau-Ginzburg theory with a negative power superpotential by a simple change
of variables, extending the known duality to the open string sector. Possible
applications to the two-dimensional noncritical string theories and
supersymmetric orientifolds in the higher dimension are also discussed.