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We study the local statistics of zeros of $L$-functions attached toArtin-Scheier curves over finite fields. We consider three families ofArtin-Schreier $L$-functions: the ordinary, polynomial (the $p$-rank 0 stratum)and odd-polynomial families. We compute the 1-level zero-density of the firstand third families and the 2-level density of the second family for testfunctions with Fourier transform supported in a suitable interval. In each casewe obtain agreement with a unitary or symplectic random matrix model.

Local Statistics for Zeros of Artin-Schreier L-functions