  We assemble a database of 12 dwarf galaxies, for which optical (R-band) and
near-infrared ($3.6\mu m$) surface brightness density together with
spectroscopic rotation curve data are available, in order to test the slowly
rotating Bose-Einstein Condensate (srBEC) dark matter model. We aim to
establish the angular velocity range compatible with observations, bounded from
above by the requirement of finite size halos, to check the modelfits with the
dataset, and the universality of the BEC halo parameter $\mathcal{R}$. We
construct the spatial luminosity density of the stellar component of the dwarf
galaxies based on their $3.6\mu m$ and R-band surface brightness profiles,
assuming an axisymmetric baryonic mass distribution. We build up the gaseous
component by employing a truncated disk model. We fit a baryonic plus dark
matter combined model, parametrized by the M/L ratios of the baryonic
components and parameters of the srBEC (the central density $\rho_c$, size of
the static BEC halo $\mathcal{R}$, angular velocity $\omega$) to the rotation
curves. The $3.6\mu m$ surface brightness of 6 galaxies indicates the presence
of a bulge and a disk component. The shape of the $3.6\mu m$ and R-band spatial
mass density profiles being similar is consistent with the stellar mass of the
galaxies emerging wavelength-independent. The srBEC model fits the rotation
curve of 11 galaxies out of 12 within $1\sigma$ significance level, with the
average of $\mathcal{R}$ as 7.51 kpc and standard deviation of 2.96 kpc. This
represents an improvement over the static BEC modelfit. For the well-fitting 11
galaxies the angular velocities allowing for a finite size srBEC halo are
$<2.2\times 10^{-16}$ 1/s. For a scattering length of the BEC particle of
$a\approx 10^6$ fm, the mass of the BEC particle is slightly better constrained
than in the static case as $m\in[1.26\times10^{-17}\div3.08\times10^{-17}]$
eV/c$^2$.
