What are rules for destroying paper and electronic health records?

Depends. Active files have no expiration date but can be thinned for convenience. Generally files over 7 years old with no clinic visits can be backfiled or destroyed. There are no rules regarding electronic medical records since there is no space issue at work. I am sure some will be issued with time as the storage space on servers starts to become full.
Medical records. Health records (paper) can be destroyed after seven years. This may differ from state to state. You may have to confirm from local medical licensing authority. Not sure about electronic records. Are they not supposed to be for ever?