Epigenetics is the study of heritable changes in gene expression or cellular phenotype caused by mechanisms other than changes in the underlying DNA sequence. Genomic imprinting is an epigenetically regulated process by which imprinted genes are expressed in a parent-of-origin-specific manner. It can be confounded with a phenomenon, allelic expression imbalance (AEI), which, in this paper, refers to asymmetric expression of the two alleles of a heterozygous subject at a single nucleotide polymorphism not caused by imprinting (non-imprinting AEI). Since existing methods in the literature are not amenable to distinguishing imprinting from non-imprinting AEI for data without replicates, we propose AIJ, a joint test for simultaneous detection of imprinting and non-imprinting AEI that accounts for potential confounding using RNA-seq data based on a reciprocal cross design. Through a simulation study, we show that AIJ is more powerful compared to two frequently used methods that do not account for confounding. To illustrate the practical utility of AIJ, we applied the method to a mouse dataset and identified genes with the imprinting effect and/or non-imprinting AEI phenomenon, with some already confirmed in an existing database. The results are also largely consistent with a study on human data for a set of orthologous genes, affirming earlier conclusion in the literature that non-imprinting AEI events are evolutionarily conserved.