In every state but one (Montana), if you don't have an employment contract that expressly states that you can only be terminated for cause, you are an at will employee.
At will employees can legally be terminated at any time, with or without cause. There doesn't have to be a reason, so they don't have to give a reason. So yes, they legally can release someone without a reason.
Now, that being said, there are some reasons which are illegal, such as termination based on race. Another potential illegal basis for termination is retaliation, but that doesn't mean every form of retaliation. It's actually very limited. For the "retaliation" law to be applicable, it will depend on just want you were complaining about because only certain types of complaints are protected complaints. Those that aren't protected are considered 'office politics' and can actually legally form a basis for termination.
The protected forms of complaint related to race, religion, gender, age, disability or FMLA use discrimination, worker's compensation claims, OSHA safety complaints or wage and hour law disputes. If your complaint to HR fits into one of those categories, then you need to file a claim of retaliation. If it was related to race, religion, gender, age or disability, contact the EEOC. If related to FMLA use or wage and hour laws, contact the Department of Labor. If related to OSHA issues, contact OSHA itself. If related to workers compensation, you'd have to file with a local WC attorney.