Depends on a lot of things ...
For most modern regulations (Europe, USA, Australia, Canada, Japan etc), in house testing is OK as long as it can stand up to auditor/reviewer checks. Use qualified people, traceable equipment, validated set ups and keep good records and there should be no problem.
Known exceptions are China and Brazil. Brazil will accept reports from accredited labs, China is a bit unclear. There may be forum members with more experience on those countries than me.
If you are looking at product certification (mark on your product), you need to check with the agency what they will accept. Some will accept manufacturer tests without much effort, some will want to witness the tests, and some might prefer to do it themselves.
Lastly there is marketing, some manufacturers prefer a third party lab report as it looks better.