The two incidents occurred on Tuesday morning and detectives believe the same two men may have carried out the crimes.
Two men were seen in the driveway of a house on Old Golf Court Road, Armadale, around 2:30am on Tuesday morning after gaining to the rear of the property.
Keys and some personal effects were stolen from the house. The householder confronted them and the men ran off towards the entrance of Old Golf Course Road.
The second theft took place around 3:30am on the same morning when the suspects had gained access to a house in Polkemmet Drive, Harthill.
The householders then discovered that a handbag and keys had been stolen. The suspects made off without the vehicle.
Detective Sergeant Cairney of Livingston Police Station said: “We believe that the same two men are responsible for these two incidents and our enquiries are continuing to trace them.
“They were both wearing dark-coloured clothing and hooded jackets. One of the men had a reflective strip on his trousers. We believe they were using a dark-coloured car.
“I would ask anyone who lives in and around these areas to get in contact with police if they saw anyone acting suspiciously or a suspicious vehicle. If anyone has personal footage that may help our investigation, please get in touch.”
Anyone with information should contact 101 with reference number 0262 of June 14. Alternatively, Crimestoppers can be contacted on 0800 555 111, where anonymity can be maintained.