Yes and no. There are certain things that non-profits must make public, and others that can be kept private, like some donors and the like. Go to their website, if they have one, and see what financials are disclsoed there, or who handles their records. You can also try the State, as it is the government entity that allows for the non-profit status to be granted in the first place. They would be able to provide you with what type of organization this is from a corporate level, and what you allowed to see, and what can be kept from the public. Hope that helps!
You are wise to check out the reliability of charities before you give. While there may be no legal requirement that the reports you seek be public, the Better Business Bureau has established voluntary accountability standards for charities, and has a list of Charities that have complied with their "Wise Giving Alliance" standards. I have attached a link.