No, I would do an investigation if I had reason to believe.... Normally, an investigation is triggered by the request of an MP. As soon as I get a complaint, I will look into it carefully and decide whether to proceed with it on the basis of whether reasonable grounds have been provided and a sufficiently explicit explanation as to what the offence is alleged to have been.
I also have the option on my own to self-initiate an investigation. I've done that a couple of times, and that's if something comes to my attention, not from an MP.