Do not release this original test notice to the testing company. Keep the original and do not presign or predate it. The testing company is only certified to test the device. Once the testing company has filled in appropriately and returned it to you, sign off and mail it in. The testing company should not mail it.
Our policy has been to mail in the test forms for the customer as a courtesy. This also helps keep a record of our test results for our customer's file because we can make a copy in our office before the original is sent out. We can no longer do this for Los Angeles County. If you get a test form from Los Angeles County, we recommend making a copy of the completed form for your records once the device has been certified. Things do occasionally get lost in the mail, and while most agencies only accept original forms, they do sometimes make exceptions and you could save yourself the trouble and expense of having to have the device retested if something does happen to the original.
So far, this is the only local agency we know of that requires this, but it wouldn't be surprising to see others follow suit.