RS-232 is a bipolar signal: -12v & +12v as spec, -6 & +6 will work. Ground is the "neutral zone", an invalid state.
The easy answer is to have the relay contacts go to request to send (RTS) & clear to send (CTS). RTS is a driven signal from data terminal equipment (DTE:the computer) and CTS is flow control from the data communication equipment (DCE: a modem). It allows the DCE to throttle data and not be overrun.
All that aside: RTS is easily directly switchable on your system & CTS is just as easily read. There are simple calls in visualBASIC for each, with equivalents in other languages.
You can also use data terminal ready (DTR) and data set ready (DSR) in exactly the same way. These are how each side senses the others' existence.
The NO or NC contacts can be used, season to taste... just be sure no voltage is in the contacts: they just switch... G.H. <<<)))