TAKE A LOOK AT YOUR FREE OPTIONS
Yes, there is 2 ways to search for criminal records for free.
The first way is to use Google. Type the following: "[name of the state] crminal records" For example, type: "new york criminal records" without the quotes. Look for websites ending with either .GOV or .US. Those are the official websites of the state that allows you do to free criminal check.
The other free way is to use a website called Criminal Searches (the link to the website is below on this page in the resources section.) This is totally free website to obtain criminal records.
If you found that the person you're suspecting is actually a criminal using the methods above or you're still suspecting there's something then doing a background check on him is a must.
HOWEVER..be careful on this. There are lots of scam background search companies out there (for a good reason, lots of people are looking to conduct searches on individuals these days so those companies see big money in this industry.) I advise you to go with a reputable company like USSearch (link below in the resources section) where for a pretty cheap price you can get a background report on someone. You can also get criminal records on NATIONWIDE level (using the methods in step 1 you can only search on state level.)
You don't have to limit your search online. Don't be afraid to call local newspapers and police stations which can provide you some valuable information. Some of the information is charges about that person (but not convictions, you need to follow up with the local court to determine whether the person was convinced of the charges.)