Primary hypoadrenocorticism, also known as Addison’s disease, is an autoimmune disorder leading to the destruction of the adrenal cortex and subsequent loss of glucocorticoid and mineralocorticoid hormones. The disease is prevalent in Standard Poodles and is believed to be highly heritable in the breed. Using genotypes derived from the Illumina Canine HD SNP array, we performed a genome-wide association study of 133 carefully phenotyped Standard Poodles (61 affected, 72 unaffected) and found no markers significantly associated with the disease. We also sequenced the entire genomes of 20 Standard Poodles (13 affected, 7 unaffected) and analyzed the data to identify common variants (including SNPs, indels, structural variants, and copy number variants) across affected dogs and variants segregating within a single pedigree of highly affected dogs. We identified several candidate genes that may be fixed in both Standard Poodles and a small population of dogs of related breeds. Further studies are required to confirm these findings more broadly, as well as additional gene-mapping efforts aimed at fully understanding the genetic basis of what is likely a complex inherited disorder.