Officers were called at around 1.40am after the resident was woken by banging noises outside their property in Foolow, Eyam.
The homeowner looked out of their window to see a man attempting to force open the door of the garage.
The man, who was described as being of stocky build, wearing a dark coloured coat, jogging bottoms, and his face covered, then jumped over a wall towards the Wardlow Mine area.
Officers investigating the incident are appealing to anyone who may have seen any suspicious activity in the area to contact them.
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Homeowners are also being encouraged to check the security of their sheds, garages and outbuilding to help further protect their property from being targeted by thieves.
Anyone with any information about the incident, or who may have seen someone acting suspiciously in the area, is asked to contact PC Gary Ferguson on 101, quoting crime number 7481/16, or Crimestoppers anonymously on 0800 555 111.
For more crime prevention advice, or to speak to the Hathersage Safer Neighbourhood Team call 101, and follow the team on Twitter: @HathersageSNT