The raiders stole house keys, a computer tablet and a mobile phone from the St Vigeans Road flat between 18:00 on Tuesday and 07:30 on Wednesday.
Thieves then returned to steal four gent's watches from the same property at about 01:00 on Thursday.
Officers have appealed for anyone who was in the area at the time to come forward.

The foxhound was deliberately run over near Conwy in February after police could not bring it under control.
The review said no action should be taken against the officers involved.
But it also recommended the force should introduce new procedures for dealing with similar incidents in future.
Traffic police drove at the dog at high speed on the dual carriageway between Llanfairfechan roundabout and the Conwy tunnel in the early hours of 22 February.
Firearms officers were sent to the scene, but there was concern they would not be able to get a safe shot.
The dog had gone missing from a hunt and police said the owner supported the force's decision.
The force voluntarily referred the incident to the Independent Police Complaints Commission because of the level of public concern.
The IPCC determined that North Wales Police should continue with its own investigation and advised on the makeup of the review panel, which included a vet, a representative of the RSPCA and a senior officer from the Metropolitan Police's Dog Support Unit.
The review has also recommended that patrol vehicles should carry slip leads and nets, which may have helped in this case.
Officers should get expert advice from dog handlers and vets if a similar situation happens again, it said.
Deputy Chief Constable Gareth Pritchard said: "It is regrettable that the dog died in this way and I fully understand the level of public concern.
"I am grateful to the panel who gave their time and expertise to carefully consider all aspects of the incident and for their diligence in coming to their conclusions and recommendations, which along with the learning points are being put in place by the force."

The Reserve Bank of Australia (RBA) cut its key rate to 2.75% from 3%.
The bank said it expected investment in the resources sector, one of its biggest drivers of growth in recent times, to peak this year.
It added that a rate cut would provide a boost to other areas of the economy and help sustain long-term growth.
"There has been a strengthening in consumption and a modest firming in dwelling investment, and prospects are for some increase in business investment outside the resources sector over the next year," the central bank said in a statement.
"These developments, some of which have been assisted by the reductions in interest rates that began 18 months ago, will all be helpful in sustaining growth."
Australia's economic growth in recent years has been fuelled by the growing demand for its commodities, such as iron ore.
That resulted in a resources boom in Australia and helped it sustain growth through the global financial crisis.
However, as demand from key markets such as China has eased, there have been concerns that Australia's mining sector may see its growth slow.
At the same time, many analysts have pointed out that other areas of the country's economy have not done so well, resulting in what many have termed a two-speed economy.
To make matters worse, the Australian currency has strengthened - making its exports more expensive, as well as affecting sectors such as manufacturing and tourism.
It rose nearly 9% against the US dollar between June 2012 and April 2013.
Amid all these concerns, there have been calls for policymakers to take steps to help boost growth, especially in the non-mining sectors, to ensure that the economy continues to grow.
Analysts said the cut in interest rates, which will help bring down borrowing costs for businesses and consumers, will help to provide some relief to those sectors and allay fears of an economic slowdown.
"Commodity prices have fallen and inflation has come in less than expected, and of course the Australian dollar through all of that has remained surprisingly strong," said Shane Oliver, chief economist with AMP Capital Investors.
"I think it was appropriate for the Reserve to provide a bit more confidence [so that] when the mining investment boom starts to wane the rest of the economy will fill the gap."
The Australian dollar weakened slightly, dipping 0.7% against the US dollar, after the rate cut was announced.
It was trading close to A$0.9808 against the US dollar in Asian trade.
Police are hunting thieves who targeted an Arbroath flat twice in the space of two days.
[NEXT_CONCEPT]
Officers were justified in using a patrol car to kill a dog running loose on the A55, a review for North Wales Police has said.
[NEXT_CONCEPT]
Australia's central bank has cut its benchmark interest rate to a record low, in an attempt to counter slowing growth in the country's mining sector.