There are a few types of crimes that may prevent naturalization. If you are seeking a police certificate for immigration purposes, the police may uncover evidence of a crime that would make you ineligible for naturalization.
For example, if you have been convicted of a serious crime, such as murder or rape, you will not be able to become a naturalized citizen. Additionally, if you have been convicted of multiple crimes, or if you have been convicted of a crime that involved moral turpitude (e.g. fraud), you may be ineligible for naturalization.
In some cases, even if you have not been convicted of a crime but there is evidence that you have committed a crime, you may be denied naturalization. Therefore, it is important to consult with an attorney before seeking a police certificate for immigration purposes to ensure that you are eligible for naturalization.
Other Legal Violations That Can Temporarily Affect Citizenship
These crimes might temporarily affect your citizenship application if they have taken place in  the last five years (or three years if the applicant is married to a U.S. citizen).
Your income is generated by illegal gambling or you’ve been convicted of two or more gambling crimes.
You’ve served five years or more in prison as a result of two or more crimes.
You’ve spent at least 180 days in jail for any crime.
You’ve committed a crime involving illegal drugs (this does not include a single offense involving 30 grams or less of marijuana).
You’ve participated in or operated a commercial vice enterprise (e.g. pornography, prostitution, etc.).