  Search for the statistical anisotropy in the CMB data is a powerful tool for
constraining models of the early Universe. In this paper we focus on the
recently proposed cosmological scenario with conformal rolling. We consider two
sub-scenarios, one of which involves a long intermediate stage between
conformal rolling and conventional hot epoch. Primordial scalar perturbations
generated within these sub-scenarios have different direction-dependent power
spectra, both characterized by a single parameter h^2. We search for the
signatures of this anisotropy in the seven-year WMAP data using quadratic
maximum likelihood method, first applied for similar purposes by Hanson and
Lewis. We confirm the large quadrupole anisotropy detected in V and W bands,
which has been argued to originate from systematic effects rather than from
cosmology. We construct an estimator for the parameter h^2. In the case of the
sub-scenario with the intermediate stage we set an upper limit h^2 < 0.045 at
the 95% confidence level. The constraint on h^2 is much weaker in the case of
another sub-scenario, where the intermediate stage is absent.
