Yes. The Centers for Disease Control and Protection (CDC) recommends hepatitis B and C testing for everyone with HIV. Testing is also advised for people born from 1945 through 1965, men who have sex with men, and those who have used injection drugs, especially if they shared any drug-related equipment.
Hepatitis C is the most common bloodborne virus. More people die as a result of hep C than from all 60 reportable infectious diseases combined. Viral hepatitis can be asymptomatic for decades, and may cause serious liver damage without you knowing it.