  Although the magnetospheric accretion model has been extensively applied to T
Tauri Stars with typical mass accretion rates, the very low accretion regime is
still not fully explored. Here we report multi-epoch observations and modeling
of CVSO 1335, a 5 Myr old solar mass star which is accreting mass from the
disk, as evidenced by redshifted absorption in the H$\alpha$ profile, but with
very uncertain estimates of mass accretion rate using traditional calibrators.
We use the accretion shock model to constrain the mass accretion rate from the
Balmer jump excess measured with respect to a non-accreting template, and we
model the H$\alpha$ profile, observed simultaneously, using magnetospheric
accretion models. Using data taken on consecutive nights, we found that the
accretion rate of the star is low, $4-9 \times 10^{-10} \,$ M$_{\odot}\,$
yr$^{-1}$, suggesting a variability on a timescale of days. The observed
H$\alpha$ profiles point to two geometrically isolated accretion flows,
suggesting a complex infall geometry. The systems of redshifted absorptions
observed are consistent with the star being a dipper, although multi-band
photometric monitoring is needed to confirm this hypothesis.
