Can my employer report something false in my personnel file?

No. If your employer does this, you can ask to have the statement corrected or removed from your personnel file.If your employer won’t take out or correct the statement, you may submit your own “explanatory statement” giving your side of the story. Your statement must stay with the personnel file.

See Conn. Gen. Stat. § 31-128e.

Also, you may have a case against your employer for defamation. If your employer knew that the statement that it put in your personnel file was false, or was reckless in determining whether the statement was false, then it may be liable for defamation. If you lost your job because of the false statement, then you may be able to collect back pay in addition to compensation for damage to your professional reputation.