They are currently treating one of the incidents as attempted murder after an 83 year old woman was found seriously injured after four men ransacked her home in the Sydney Street area of Aughnacloy, Co Tyrone shortly after 9 pm on Tuesday.
The elderly woman was discovered lying injured in the garden of her home and remains in a critical but stable condition in hospital.
The four suspects made off in a black coloured car in the direction of Moore Street.
Police are investigating a possible link between the incident and three other reported burglaries which occurred in Aghaloo Close in Aughnacloy, Richmond Park in Ballygawley and in McDowell Terrace in Seskinore on Tuesday, as well as a separate report of a similar suspicious vehicle.
Detective Chief Inspector John Caldwell said: “We are continuing to investigate this appalling incident in which a vulnerable 83 year old woman sustained serious injuries and the other burglaries which we believe are linked.
“We have made progress and would now like to make a specific appeal for anyone who has information about two cars which may have been in the location of the burglaries over recent days.
“We are seeking information about a dark coloured car bearing the registration GK56 AEG, and a silver car, possibly a Ford Focus, with registration 06WX 6313.
“We believe at this stage these were both false registration plates.
“I am appealing for anyone who has any information about these cars or about the burglaries to contact detectives in Dungannon.
“We have set up an incident room in Dungannon to deal with any information.
“Please call 101 ex 53135 quoting reference 1218 of 23/01/18. Alternatively, information can also be provided about either incident to the independent charity Crimestoppers on 0800 555 111 which is 100% anonymous and gives people the power to speak up and stop crime.”