Christopher Johnson (45) is alleged to have stolen clothes and other personal items from a car belonging to the couple while it was parked at a hotel in the north of the city.
Judge Bernadette Owens granted him bail when he appeared in Dublin District Court.
The case was adjourned for the directions of the DPP.
Mr Johnson, of The Botanic, Prospect Hill, Finglas, is charged with theft of the property including clothes, a guitar and laptop, as well as criminal damage to the car, on March 24.
The break-in is alleged to have happened in the underground car park at the Travel Lodge Hotel, Shangan Road, Ballymun.
Separately, Mr Johnson is also alleged to have damaged and taken property from another car parked at the same location.
Garda Andy McDonnell said he arrested the accused at The Plaza, Ballymun at 1.45pm yesterday and brought him to Ballymun station.
He was charged there at 5.51pm yesterday and made no reply to any of the counts after caution. He was handed copies of the charge sheets.
Gda Johnson did not object to bail subject to conditions.
Judge Owens granted bail in the accused’s own bond of €300 with no cash lodgement required.
Under conditions, Mr Johnson must sign on three times per week at Ballymun Garda Station, observe a nightly curfew between 11pm and 6am and stay away from the Travel Lodge hotel in Ballymun.
The garda had initially requested a daily sign on condition “to keep an eye on” the accused and that he was complying with bail conditions. Judge Owens said three days should be sufficient.
The judge granted free legal aid following an application by defence solicitor John Heaney, who said Mr Johnson was unemployed.
The defence agreed to the bail conditions, he said.
Gda McDonnell said DPP directions were outstanding.
Judge Owens remanded the accused on bail to appear in court again on May 17.
The accused has not yet indicated how he intends to plead to the charges, which are under the Theft and Fraud and Criminal Damage Acts.
Gardai have said the property is still missing but efforts to recover it are continuing.
The Ukrainian refugees whose car was allegedly broken into had fled their Kyiv home in the early days of Russia’s invasion of Ukraine.
They drove through a number of countries before arriving in Ireland just two weeks before the alleged theft.
The couple said they were surprised to be stolen from, as there were Ukrainian plates on the car and “the whole world knows about Ukraine.”
"It was obvious we are refugees and this is all we have,” one of the alleged victims said.
It was not possible for them to get their insurance to cover the cost of the missing items, but over €15,000 has been raised for them on a GoFundMe page.