No, you cannot sue for defamation or slander. Defamation and slander are for untrue statements that say bad things about you ... that you cannot do your job or you committed a crime. According to your statement .. the police officers lied and said you DIDN'T commit a crime. I know you probably want to help your boyfriend, but it is not the wisest thing to keep pushing the fact that you are guilty. Talk to his attorney and stop making admissions online.