Albert Barnes Commentary Acts 16:38

"And the sergeants reported these words unto the magistrates: and they feared when they heard that they were Romans;" — Acts 16:38 (ASV)

They feared, when they heard, etc. They were apprehensive of punishment for having imprisoned them in violation of the laws of the empire.

To punish a Roman citizen unjustly was deemed an offence to the majesty of the Roman people and was severely punished by the laws. For example, Dionysius of Halicarnassus (Roman Antiquities, Book 2) says that "the punishment appointed for those who abrogated or transgressed the Valerian law was death, and the confiscation of his property."

Furthermore, the emperor Claudius deprived the inhabitants of Rhodes of their freedom for having crucified some Roman citizens (Dio Cassius, Book 60). (See also Kuinoel and Grotius.)

The "serjeants" mentioned in the account were "officers."