Is it necessary to have only recommendations from Computer Science professors for an application to Computer Science grad program? Can I also have my finance/economics professor recommend me? I have a good relationship with her. Would it matter if she isn't from the CS department in my college?
Yes, absolutely.  Your references should be people who know you, your work and your capabilities best and can give the admissions committee the best possible insight into what to expect from you.  That matters a lot more than what department they're in.  For that matter, they don't even have to be former instructors.  You might also turn to a former supervisor at an internship you did one summer if the work you did for them was especially impressive.