  In this article we explore the critical end point in the $T-\mu$ phase
diagram of a thermomagnetic nonlocal Nambu--Jona-Lasinio model in the weak
field limit. We work with the Gaussian regulator, and find that a crossover
takes place at $\mu, B=0$. The crossover turns to a first order phase
transition as the chemical potential or the magnetic field increase. The
critical end point of the phase diagram occurs at a higher temperature and
lower chemical potential as the magnetic field increases. This result is in
accordance to similar findings in other effective models. We also find there is
a critical magnetic field, for which a first order phase transition takes place
even at $\mu=0$.
