zone inputs going to the Arduino as well.
Alarm systems normally run a current loop through a small resistor for each zone. Normally-closed sensors are wired in series with one another across the zone inputs. Normally open ones are wired in parallel across the inputs. An open circuit on a normally-closed sensor will drop the current in the circuit to 0 and the alarm condition will be detected. A short circuit in a normally-open sensor will cause a current rise, and the alarm condition will be detected.
To snoop this, you will have to put a voltage sensor -- and it could be an A2D input or a comparator circuit -- on the zone connections of the alarm system and look at how the voltages change with open/short conditions. Normally there is a very wide range of currents that are accepted as "no alarm" by the system -- maybe from 1 mA through 100 mA -- a short brings the current above 100mA and an open drops it below 1mA. Finding the corresponding magic voltage levels at the alarm system terminals will take some trial and error.
The installation manual for your alarm system unit is likely available online, and you will get better information from that.