The cannot go against state statutes if the statutes deny the court jurisdiction. However, I am willing to bet that you are misinterpreting the statutes. The Constitution of the United States guarantees every citizen the right to petition the government (i.e. the courts) for a redress of grievances. This acts as a bar to the legislature from denying access to the courts. However, due to increasing cases loads, many courts around the country have created alternative dispute resolution programs to decrease the burdens on the courts. These ADR programs are constitutional because they are voluntary. However, they never bar an aggrieved party from accessing the courts. The only exception to this is when the state has developed a quasi-judicial agency that will hear the claim. In this case, the state can require that you go through the administrative process BEFORE going to court. However, again, most states do not mandate the administrative process. Rather, many tenants prefer the administrative process because you do not need to hire an attorney to use it. If you want to cite the statute that you are referring to, I will give you a more specific answer to your question.