You cannot write to CTS and DSR because Labview serial interface acts like DTE equipment (Data Terminal Equipment, like a terminal). DTE affects RTS and DTR. In comparison DCE equipment (Data Communications Equipment, like a computer that a terminal connects to) affects CTS and DSR. In order to affect those lines with Labview, you would have to use a null modem cable, sometimes called a crossover cable, which swaps RTS and CTS pins, and swaps DSR and DTR pins (also swaps TD and RD pins). Then you could change the state of RTS to actually change CTS, and change DTR to actually change DSR. Is this clear?
Since your device needs RTS as an input, it is a DCE device. Usually a DCE device sees RTS (Request To Send)and grants CTS (Clear to Send)if it is ready to
receive data. Why do you want to control CTS or DSR (outputs from DCE) if your device is already DCE?