Chesterfield are studying CCTV footage of City fans from Saturday's game at the Proact Stadium.
Some supporters spilled on to the pitch and there were several ejected from the ground. Punches were also thrown with stewards after the final whistle.
Chesterfield stadium manager Colin Nellist said: “CCTV footage will be studied - as it is after every match - and the evidence will be used to take appropriate action against anyone found guilty of breaking the law.
“In order to ensure a safe environment, we speak to the police and officials from opposition clubs in the build-up to matches. We will liaise with the police and Bradford City officials regarding this matter.”
City have declined to comment on the matter.
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