The police can charge you with a 4th degree offense for false swearing and/or providing false information to the police. A 4th degree is a felony, however there is no presumption of incarceration for a first-time offender. Further, you may be eligible (depending upon your record and circumstances) for a diversionary program which would prevent you from having a criminal record.
Best of luck!
Adam S. Malamut, Esq.