As mentioned previously a contact approach is a 'break-away' from an IFR instrument approach (differs from a visual approach in that wx minima etc are different). I think it's also a procedure or expression used in N. America.
I remember briefly touching upon them on an IFR Written Test brush up course given by Aero Course in Canada. Our instructor was a C-130 RCAF SAR pilot and he was very weary of such procedures advising us against them. I guess one of the main hazards is inadvertently entering IMC again! To quote (para-phrasing) " I've had many a call out for look for aircraft that have last called a 'contact approach'".
Just as an aside, he said that whenever he gets an alert that an a/c is overdue the first places they start looking are those few miles in and around the departure and destination airfield as usually that's where the a/c will be !!