  The disruption of a star by a supermassive black hole generates a sudden
bright flare. Previous studies have focused on the disruption by single black
holes, for which the fallback rate decays as~$\propto t^{-5/3}$. In this paper,
we generalise the study to the case of a supermassive black hole binary
(SMBHB), using both analytical estimates and hydrodynamical simulations,
looking for specific observable signatures. The range of binary separation for
which it is possible to distinguish between the disruption created by a single
or a binary black hole concerns typically separations of order a few
milliparsecs for a primary of mass $\sim 10^6M_{\odot}$. When the fallback rate
is affected by the secondary, it undergoes two types interruptions, depending
on the initial inclination $\theta$ of the orbit of the star relative to the
plane of the SMBHB. For $\theta \lesssim 70^\circ$, periodic sharp
interruptions occur and the time of first interruption depends on the distance
of the secondary black hole with the debris. If $\theta \gtrsim 70^\circ$, a
first smooth interruption occurs, but not always followed by a further recovery
of the fallback rate. This implies that most of the TDEs around a SMBHB will
undergo periodic sharp interruptions of their lightcurve.
