It sounds like you may be asking for the reverse of this, but when denial of something specific raises suspicion, an applicable phrase is "The lady doth protest too much, methinks", which is a reference to Shakespeare's Hamlet.
It implies that the denial itself is suspicious because if nothing weird was going on you wouldn't have to deny it.
For example, if you walk into your kitchen and a person says, "I didn't steal any of your cookies", you would probably be suspicious, and you could respond, "The lady doth protest too much, methinks".
Note: This is sometimes formulated "Methinks the lady doth protest too much", but that is technically a misquote