  A characterisation of initial data sets for the Schwarzschild spacetime is
provided. This characterisation is obtained by performing a 3+1 decomposition
of a certain invariant characterisation of the Schwarzschild spacetime given in
terms of concomitants of the Weyl tensor. This procedure renders a set of
necessary conditions --which can be written in terms of the electric and
magnetic parts of the Weyl tensor and their concomitants-- for an initial data
set to be a Schwarzschild initial data set. Our approach also provides a
formula for a static Killing initial data set candidate --a KID candidate.
Sufficient conditions for an initial data set to be a Schwarzschild initial
data set are obtained by supplementing the necessary conditions with the
requirement that the initial data set possesses a stationary Killing initial
data set of the form given by our KID candidate. Thus, we obtain an algorithmic
procedure of checking whether a given initial data set is Schwarzschildean or
not.
