  We study the capability of the space-based gravitational wave observatory
TianQin to test the no-hair theorem of General Relativity, using the ringdown
signal from the coalescence of massive black hole binaries. We parameterize the
ringdown signal by the four strongest quasinormal modes and estimate the signal
to noise ratio for various source parameters. We consider constraints both from
single detections and from all the events combined throughout the lifetime of
the observatory, for different astrophysical models. We find that at the end of
the mission, TianQin will have constrained deviations of the frequency and
decay time of the dominant 22 mode from the general relativistic predictions to
within 0.2% and 1.5% respectively, the frequencies of the subleading modes can
be also constrained within 0.3%. We also find that TianQin and LISA are highly
complementary, by virtue of their different frequency windows. Indeed, LISA can
best perform ringdown tests for black hole masses in excess of $\sim 3\times
10^6 M_\odot$, while TianQin is best suited for lower masses.
