In 1967 the borough of Hartlepool was removed from the administrative county when it merged with West Hartlepool to form a new county borough of Hartlepool , and in 1968 Billingham was included within the boundaries of the county borough of Teesside , associated with the North Riding . In 1967 the former area of the borough of Hartlepool was removed from the administrative county when it merged with West Hartlepool to form a new county borough of Hartlepool .