In some cases, the Project Manager has the direct authority to approve minor change requests; however, in most cases the Project Manager will need to seek CRF approval from the Project Board.
However, you should error on the side of caution. Just because the Project Manager found no issues with the constraints (schedule, cost, etc.) doesn't necessarily mean there might be an unforeseen impact on the project. Even a seemingly trivial change might cause issues down the road, so at the very least you should communicate the change to every affected team member stakeholder.
So, the answer is yes and no. If there is no definite course of action listed in the change plan based on the impacts of the change, it’s up to the PMs best judgement.