NHS Lothian contacted 25,000 people aged between 45 and 64 in some of Edinburgh's most deprived areas.
And while there was a reasonably good take-up of the free test under the Scottish Government's Keep Well scheme, 3,500 refused.
The figures have highlighted the uphill struggle health chiefs face in convincing the Capital's most at-risk patients to improve their own health.
The tests – part of a 25 million national scheme – include screening for diabetes and heart problems, as well as appropriate interventions where problems are found, and access to mental health support.
Edinburgh has severe disparities when it comes to health.
Keep Well is one of many schemes local NHS bosses have to improve health in impoverished areas.