This thread is in an ISO 13485 section, perhaps implying a non-USA rules orientation for the OP's question, but the use of the terminology "DHR" sounds as if US FDA compliance may be involved.
Some records must be signed to indicate authorization, approval or responsibility. In general, FDA does not regard a simple copy or scan of a signature as having the same legal significance as the original physical signature. Therefore a simple copy or scan of a signed record is
not equivalent to the original record.
The response prior to this one omits consideration of the FDA's stance on digital copies of records that contain a signature. Assuming that the records in your DHR all contain signatures:
If you are retain them digitally, then they are retained records.
In general this is incorrect, unless the digital system is Part 11 compliant...which is somewhat difficult and expensive to accomplish.
Destroy the hard copies as soon as the files are scanned in a logical, obtainable file structure.
This is very definitely incorrect, unless again the digital system is Part 11 compliant.
Assuming you have a backup system, this is actually more secure than just hard copies and should satisfy any auditor.
For a US FDA inspection, either QSIT 1/2 or For Cause, the last four words will be incorrect if the conditions above are not met.
See 21CFR Part 11 for the rules regarding digital copies of paper records, and digital keeping of mandated records in general.