If there was indeed no warrant and you were held without more, you may have a civil law suit. If there was an old warrant that had not been purged, that will be a more difficult or unsuccessful case. 8 hours in jail with your baby (?) is worth something if you are successful, but you will not become wealthy. Consult and attorney. Remember that you must file a notice of claim within 90 days of the incident with each municpal agency you intend on suing.
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Consult with an attorney right away regarding wrongful arrest, false arrest and possibly malicious prosecution. Value odd case depends upon the damages . Limited statute of limitation. See a local lawyer soon.
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This could be a tough case... the issue is not whether you were innocent but whether the police had probable cause to arrest you. Seeing you go through the emergency exit could give the police probable cause. Consult a civil rights lawyer ASAP. There is a 90 day time period to serve a Notice of Claim.
I am a former federal and State prosecutor and now handle criminal defense and personal injury/civil rights cases. Feel free to check out my web site and contact me at (212) 577-9797 or via email at Eric@RothsteinLawNY.com. I was named to the Super Lawyers list as one of the top attorneys in New York for 2012. No more than 5 percent of the lawyers in the state are selected by Super Lawyers. The above answer is for informational purposes only and not meant as legal advice.