Several people, including activists Kirsten Han and Rocky Howe, are under investigation for three public assemblies held outside Changi Prison Complex and in nearby Mariam Walk.
In a statement on Sunday (June 26), the police said Ms Han and Mr Howe were interviewed on Friday as part of investigations into the assemblies.
T-shirts with anti-death penalty slogans that Ms Han and Mr Howe wore on the day of the interview were relevant to the probe, the police added in response to queries.
Both Ms Han and Mr Howe had agreed to hand them over after they were told the T-shirts would be required for investigations, the statement said.
The police also said they were advised by the Attorney-General's Chambers (AGC) to investigate if any further offences had been committed by Ms Han and Mr Howe, who are both Singaporean.
"In response to specific media queries, the police can confirm that the AGC, having reviewed the facts, has advised that Ms Han and Mr Howe did not commit any offences, by reason of the T-shirts they wore, when they came for the police interview," the police added.
When asked, the police declined to say who else is being investigated for the three public assemblies, citing the ongoing inquiry.
The police also did not say when the assemblies were held.
In several online posts last week, Ms Han, who is a freelance journalist, said she and Mr Howe were questioned over allegations that they had taken part in two public assemblies without a permit between March 29 and April 25.
Taking part in a public assembly without a police permit is illegal in Singapore and is an offence under the Public Order Act. First-time offenders can be fined up to $3,000, while repeat offenders face a fine of up to $5,000.
According to Ms Han, police said the first alleged illegal assembly was when she and three others had gathered outside Changi Prison the night before 68-year-old Singaporean Abdul Kahar Othman was hanged for drug trafficking on March 30.
The second alleged illegal assembly was when Ms Han and three others had posed for photos outside Changi Prison two nights before the execution of Malaysian Nagaenthran K. Dharmalingam on April 27, she added.
For these alleged offences, Ms Han, who is in her 30s, and Mr Howe, who is in his 20s, were interviewed at Bedok Police Division Headquarters on June 24.
Ms Han said the anti-death penalty T-shirts she and Mr Howe wore to the interview were confiscated by the police, who allegedly claimed that the pair had participated in an illegal procession because they walked across the street to the police station while wearing them.
Writing in her online newsletter on Saturday, Ms Han added: "I was made to call our friend Soh Lung, who was waiting for us in the foyer, to get her to go to the market to buy us new shirts, so that we could change and surrender our T-shirts."
She was referring to Ms Teo Soh Lung, a former political detainee who has also been posting updates about the investigation into Ms Han on social media.
In her post, Ms Han also took issue with a police officer who had asked that she surrender her social media accounts and provide the police with the passwords to access them.
This was after Ms Han had agreed to surrender her phone, but not before she had logged out of, or uninstalled, her social media applications.
Ms Han said when she refused, she was warned that Section 39 of the Criminal Procedure Code (CPC) "might come into play".
The police, in their statement on Sunday, said only that Ms Han's and Mr Howe's mobile phones were seized for forensic examination as part of investigations.
Under Section 39 of the CPC, police officers have the power to access, inspect and check the operation of a "computer" used in connection with an arrestable offence.
The police officer may also order persons using, or who have used, the computer to assist the police in gaining access to it, including providing any username, password or other authentication information required.
Any person who obstructs the lawful exercise of any power under the section by a police officer, or fails to comply with an order under it, can be fined up to $5,000, jailed for up to six months, or both.