Mr Mouat, 64, was last seen at his home address in Panbrae Road, Bo'ness on the evening of Thursday 6 July 2017. His body was found on Saturday 5 August 2017 at his home.
The PIRC investigation will focus on the initial response from Police Scotland including the search of his home address.
The investigation is in the very early stages and a report will be sent to the Chief Constable in due course.
In a statement issued through the PIRC, the family of Mr Mouat said:
"As a family we are devastated by the loss of a loving husband and father and we are now trying to come to terms with what has happened.
"We would like to thank everyone for the support we have received over these last few difficult weeks but would now ask for our privacy to be respected so that we have the time and space to grieve in peace."