Charlotte Murray, 34 and originally from Omagh, was reported missing in May but has not been in contact with her family or friends since November.
"Charlotte is a free spirit who likes to do her own thing, but this is out of character," her twin sister Denise said.
"She moved to Moy a few years ago and we were not in regular contact. All the family are worried that she hasn't been in contact with any of us. We are very worried.
Charlotte is described as being 5ft 4ins tall and of slim build, with a pale complexion, blue eyes and brown hair - although she has been known to change her hair colour.
Police have now set up a special telephone number for anyone with information about the missing woman's whereabouts and are conducting a leaflet drop as part of their ongoing enquiries.
We want Charlotte to get in touch so that we know she's okay.
Charlotte's sister Denise
PSNI area commander for Dungannon and Cookstown, Chief Inspector Jane Humphries, said:"Despite several enquiries over the past two months, police have been unable to make contact with Charlotte. A previous appeal for information in May did not put her in touch with us.
"We are becoming increasingly concerned for Charlotte's safety."
Chief Inspector Humphries added: "I have three appeals. The first is to Charlotte: if you see this or hear this appeal, please get in touch.
"Present yourself to police, at any station, so that we can establish that you are safe.
"The second is to anyone who thinks they may have seen or spoken to Charlotte at any time since last October or November. We need to know when and where this encounter took place and what Charlotte was doing.
"Thirdly, we are appealing to anyone who knows where Charlotte is now or what might have happened to her. We need you to contact police for Charlotte's sake and for the sake of her family who are becoming increasingly anxious."
The special telephone number for anyone with information about Charlotte is 028 37 517390.