You should get a company who is certified in ISO 13485 to do the assembly for you as assembly of a medical device falls into part of the manufacturing process of a medical device. Since you are handling the design and development of the device, this will also fall into part of the process which ISO 13485 covers. The scope of ISO 13485 covers design and development, manufacturing, distribution, servicing and installation activities of medical devices. Getting ISO 13485 would help you to obtain regulatory approvals and clearance for your marketing activities in the future.
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