  Gravitational-wave (GW) observations of binary black holes offer the best
probes of the relativistic, strong-field regime of gravity. Gravitational
radiation, in the leading order is quadrupolar. However, non-quadrupole
(higher-order) modes make appreciable contribution to the radiation from binary
black holes with large mass ratios and misaligned spins. The multipolar
structure of the radiation is fully determined by the intrinsic parameters
(masses and spin angular momenta of the companion black holes) of a binary in
quasi-circular orbit. Following our previous work \cite{Dhanpal:2018ufk}, we
develop multiple ways of testing the consistency of the observed GW signal with
the expected multipolar structure of radiation from binary black holes in
general relativity. We call this a "no-hair" test of binary black holes as this
is similar to testing the "no-hair" theorem for isolated black holes through
mutual consistency of the quasi-normal mode spectrum. We use Bayesian inference
on simulated GW signals that are consistent/inconsistent with binary black
holes in GR to demonstrate the power of the proposed tests. We also make
estimate systematic errors arising as a result of neglecting companion spins.
