The Appraiser and Property requirements for Title II forward and reverse mortgages are in Handbook 4000.1 II.D.
Additional requirements for the Standard 203(k) and Limited 203(k) Rehabilitation Mortgages are in Handbook 4000.1 II.A.8 and 4000.1 II D.12.c
For additional information see Handbook 4000.1 II.D, II.A.8. and II.D.12.c available at https://www.hud.gov/program_offices/administration/hudclips/handbooks/hsgh
Instructions detailing specific requirements for reporting the results of the appraisal are found in the FHA Single Family Housing Appraisal Report and Data Delivery Guide at https://www.hud.gov/program_offices/housing/sfh/handbook_references