According to a book I read ci is pronounced chi. I don't know if it's my hearing but why do I hear sh in the TV show Gomorra? Is there an sh regional variant maybe?
The standard pronunciation of Italian ci (unless there is a s before it) is /tʃi/ (which is approximately like the initial sounds of English word “cheap”). In some regional variants (Tuscany, Lazio, parts of Southern Italy) it is quite usual to pronounce it, only when it follows a vowel, like /ʃi/ (the initial sound of “sheen”, say).
The same applies to ce (standard pronunciation with /tʃ/, regional pronunciation after a vowel with /ʃ/).
The regional sound is similar to that which in standard Italian is denoted by sci (or sce), the difference being that in the latter the /ʃ/-sound, after a vowel, is geminated (i.e. stronger, doubled). For instance, the standard pronunciation of the word pece (“pitch”, the substance) is /'petʃe/, its regional pronunciation can be /'peʃe/, while the word pesce (“fish”) is pronounced mostly everywhere /ˈpeʃːe/ (also denoted /ˈpeʃʃe/).