I agree with what has already been said. You should go with a trusted friend or family member for a roomate, but then again it could be disastrous because you dont really know a person until you have lived with them.
But if you must search for a roomate - try a co-worker, church member, classmate, or a club member. For the above mentioned, you should know them for at least a year so you can get a good idea of whether or not you should approach them with the offer instead of wasting your time.
But ALWAYS treat this as if you are hiring someone to work for you. Make them fill out an application, pass a FEDERAL background check, as well as a state background check, job history (stable to me means theyve had the same job for at least 5 years or more). Also you might consider a drug test since you probably dont want to have your roomate selling illicit substances out of your home or cooking in your kitchen. I know this sounds really over the top, but when your'e inviting someone to come live with you, I dont think you can never be too careful.
Also as a precaution, keep the originals of important documents such as W2s, tax returns, birth certificates, and social security cards (even your passports) in a locked secure box AWAY from your residence in a bank. Keep notarized copies in a good sturdy fireproof, floodproof safe in your home that is bolted to the floor. This way your personal information is kept confidential and out of reach of sticky hands.