When you suspect that a dog or cat could have allergic dermatitis, you need to rule out resembling diseases. Simple tests such as cytology and skin scrapes can identify other diseases that could be causing pruritus (e.g. fleas, sarcoptic mange, demodicosis, Cheyletiella, lice) as well as secondary 'flare' factors that contribute to pruritus (e.g. pyoderma, Malassezia).
Here is a list of basic procedures that can be conducted to help reach a diagnosis for atopy:
References: 1. Favrot C. J Feline Med Surg (2013);15:778-784. 2. DeBoer D. Vet Immunol (2001). 3. Hnilica KA. Small Animal Dermatology, 3rd edition, p22-36.