In practice, it often occurs that some covariates of interest are not measured because of various reasons, but there may exist some auxiliary information available. In this case, an issue of interest is how to make use of the available auxiliary information for statistical analysis. This paper discusses statistical inference problems in the context of current status data arising from an additive hazards model with auxiliary covariates. An empirical log-likelihood ratio statistic for the regression parameter vector is defined and its limiting distribution is shown to be a standard chi-squared distribution. A profile empirical log-likelihood ratio statistic for a sub-vector of the parameters and its asymptotic distribution are also studied. To assess the finite sample performance of the proposed methods, simulation studies are implemented and simulation results show that the methods work well.