  We present experimental evidence showing that the effective carrier diffusion
length ($L_d$) and lifetime ($\tau$) depend on the carrier density in
MAPbBr$_3$ single crystals. Independent measurements reveal that both $L_d$ and
$\tau$ decrease with an increase in photo-carrier density. Scanning
photocurrent microscopy is used to extract the characteristic photocurrent
$I_{ph}$ decay-length parameter, $L_d$, which is a measure of effective carrier
diffusion. The $L_d$ magnitudes for electrons and holes were determined to be ~
13.3 $\mu$m and ~ 13.8 $\mu$m respectively. A marginal increase in uniform
light bias ($\leq 5 \times 10^{15}$ photons/cm$^2$) increases the modulated
photocurrent magnitude and reduces the $L_d$ parameter by a factor of two and
three for electrons and holes respectively, indicating that the recombination
is not monomolecular. The $L_d$ variations were correlated to the features in
photoluminescence lifetime studies. Analysis of lifetime variation shows
intensity-dependent monomolecular and bimolecular recombination trends with
recombination constants determined to be ~ 9.3 $\times 10^6$ s$^{-1}$ and ~ 1.4
$\times 10^{-9}$ cm$^{3}$s$^{-1}$ respectively. Based on the trends of $L_d$
and lifetime, it is inferred that the sub-band-gap trap recombination
influences carrier transport in the low-intensity excitation regime, while
bimolecular recombination and transport dominate at high intensity.
