  The high energy emission of rotation powered pulsars is supposed to be
produced in "gaps" in the pulsar magnetosphere where charges are accelerated
and currents are produced. The rest of the magnetosphere is supposed to be
mostly a "force-free" plasma without any currents. Two important currents are
the main current that flows away from the pulsar, that produces the observed
radiation, and the current that returns to the pulsar to maintain charge
neutrality. This work attempts to study the return current in the Crab pulsar
using the soft X-ray data from the {\it{NICER}} observatory. It is assumed that
the two currents vary as a function of time. This would modulate the electric
fields in the "gaps", which would affect the observed X-ray flux. These flux
variations will show up only in the on-pulse phases, while those caused by the
Crab Nebula, instrumental effects, etc. will be present in the off-pulse phases
also. This work obtains the correlation coefficient of the flux variations in
the two peaks of the Crab pulsar, after removing the off-pulse flux variations.
No correlation was observed; its error of $0.000012$ sets an upper limit of
$0.036\%$ on the rms variation of correlated X-ray flux in the Crab pulsar.
Reasons exist for the return current variations to be correlated, while the
main current variations are probably uncorrelated. So the above number is
considered an upper limit on correlated return current variations, which may be
an important constraint for pulsar magnetospheric structure.
