Police in Chaugachha arrested Arafat Hossain Rabby after an HSC student filed a rape case against him.
Police said he was detained at about 9pm on August 1 after a written complaint was filed.
The complainant alleged that Rabby offered help with a national identity card application, took her to Chaugachha town and sexually assaulted her.
Case narratives identify different alleged locations for the incident: a rented residence in one account and another woman's home in the other.
Chaugachha police said the student was sent to Jashore General Hospital for a medical examination and that Rabby was to be sent to court.
A local student-organisation official said Rabby held a college-unit post, denied the allegation and alleged that the families had been in conflict for 15 years.
In a separate incident, detective police said they arrested 35-year-old Ujjwal during a late-night operation at a flat in the Shashtitala area of Jashore town.
Police said they seized a set of clothing described as Border Guard Bangladesh uniform, two working walkie-talkies, handcuffs, two machetes and an axe described as Chinese-made.
An additional police superintendent said investigators were examining how Ujjwal obtained the items and whether they were meant for impersonating law-enforcement personnel.
Police said the items were seized and legal action was being initiated.