  We use the Giant Metrewave Radio Telescope (GMRT) Cold-HI AT $z\approx1$
(CAT$z1$) survey, a 510 hr HI 21cm emission survey of galaxies at
$z=0.74-1.45$, to report the first measurements of atomic hydrogen (HI) scaling
relations at $z\approx1$. We divide our sample of 11,419 blue star-forming
galaxies at $z\approx1$ into three stellar mass ($M_*$) subsamples and obtain
detections (at $\geq 4\sigma$ significance) of the stacked HI 21cm emission
signal from galaxies in all three subsamples. We fit a power-law relation to
the measurements of the average HI mass ($M_{HI}$) in the three stellar-mass
subsamples to find that the slope of the $M_{HI}-M_{*}$ relation at $z\approx1$
is consistent with that at $z\approx0$. However, we find that the
$M_{HI}-M_{*}$ relation has shifted downwards from $z\approx1$ to $z\approx0$,
by a factor of $3.54\pm0.48$. Further, we find that the HI depletion timescales
($t_{dep,HI}$) of galaxies in the three stellar-mass subsamples are
systematically lower than those at $z\approx0$, by factors of $\approx2-4$. We
divide the sample galaxies into three specific star-formation rate (sSFR)
subsamples, again obtaining $\geq 4\sigma$ detections of the stacked HI 21cm
emission signal in all three subsamples. We find that the relation between the
ratio of HI mass to stellar mass and the sSFR evolves between $z\approx1$ and
$z\approx0$. Unlike the efficiency of conversion of molecular gas to stars,
which does not evolve significantly with redshift, we find that the efficiency
with which HI is converted to stars is much higher for star-forming galaxies at
$z\approx1$ than those at $z\approx0$.
