We present coreference annotation on parallel Czech-English texts of the Prague Czech-English Dependency Treebank (PCEDT). The paper describes innovations made to PCEDT 2.0 concerning coreference, as well as coreference information already present there. We characterize the coreference annotation scheme, give the statistics and compare our annotation with the coreference annotation in Ontonotes and Prague Dependency Treebank for Czech. We also present the experiments made using this corpus to improve the alignment of coreferential expressions, which helps us to collect better statistics of correspondences between types of coreferential relations in Czech and English. The corpus released as PCEDT 2.0 Coref is publicly available.