Alon-Tarsi number of signed planar graphs

Let $(G,\sigma )$ be any signed planar graph. We show that the Alon-Tarsi number of $(G,\sigma )$ is at most 5, generalizing a recent result of Zhu for unsigned case. In addition, if $(G,\sigma )$ is $2$-colorable then $(G,\sigma )$ has the Alon-Tarsi number at most 4. We also construct a signed planar graph which is $2$-colorable but not $3$-choosable.