Continental's res host is at Charlotte, NC, outsourced to EDS, and it is locked into that arrangement for at least two more years. Yes, it seems strange that carriers that otherwise have close business ties become competitors in the distribution end of things, but those anomalies exist throughout the industry. KLM is an owner of Galileo, NW is an owner of Worldspan, and neither seems to fret about that difference. Amadeus is a joint venture of Air France, Iberia, Lufthansa and others. EDS maintains its contract to run System One.
Terms are important here.
If by CRS you mean central reservation system, this is handled by Advantis since the dissolution of Gemini. Galileo is still using its Denver center, but they are migrating agencies from APG to the same Apollo system used by US agencies.