Is there a reaction between CuSO4 + KI? When I performed the reaction, a brown and yellow color was formed but when I wrote out the molecular equation, I did not find a precipitate or gas evolution.

When you write the equation there is no "apparent" reaction; however, there is a redox reaction. Cu^+2 is reduced to Cu^+2 and I^- is oxidized to I2. Cu^+1 and I^- form a ppt of CuI. The yellow brownish color probably is iodine. You may not see all of this happening unless it is in a quite acid solution AND unless there is a large excess of KI; however, Cu makes an excellent primary standard for the standardization of thiosulfate solution (which are subsequently used to titrate liberated Iodine).