Police responded to a report of two women arguing in the company of a nine-month-old baby on Quay Road at Bridlington just before midnight on August 4.
Humberside Police said the baby and a police officer suffered minor injuries.
A Humberside Police spokesman said: "Officers arrested a 31-year-old Bridlington woman on suspicion of being drunk in charge of a child.
"Once in police custody the woman is then alleged to have assaulted a police officer. While our investigations continue the woman has been released under investigation."
"If you witnessed the women fighting or anything that would help with our enquires please call the non-emergency number 101 quoting log 17 of 05/08/17."