You have at least a couple of choices:
- Do not hook up the rain sensor and exclusively make use of the weather stations that likely exists in the area.
- Hook up the sensor and use the very local information as to whether it is raining or not.
Deciding is obviously up to you. Part of it may depend on how close the weather stations are to you and how accurately they compare to reality for your yard.
I found the manual (link is below) and appears to have two way to hook it up (if you so choose, but between these two, I would do the first option):
- The old controller uses the SENSOR terminals which is for one sensor. The Rachio uses S1 and S2 terminals, which are for two sensors. So, you would use one wire going to S1 and the other going to power. According to Rachio 3 and Rainbird RSD-BEx - Accessories & Sensors / Rain Sensors - Rachio Community, you would hook the other to -24V.
- Between the common terminal and all of the commons used for the valves
P.S. I made a correction to my original post.