Air Carrier Captain reported the flight may have inadvertently transported undeclared Hazmat cargo. At destination arrival he realized there was no departure Dangerous Good Form verification completed.

Narrative

I believe there is a possibility we may have inadvertently flown a flight (ZZZ1-ZZZ) without the required Dangerous Goods Form paperwork onboard. After we landed in ZZZ; something prompted me to look at the Dangerous Goods Form area on the load sheet printout for that leg. I thought I had recalled seeing a YES next to it and; in fact; had even placed a checkmark next to it. I believe I had gotten distracted during the crosscheck and had intended to return to this and ask the ground crew about Dangerous Goods Forms; but I failed to do so. At this point; I do not know if there was hazmat on board or not.I believe we should incorporate a specific question to the loading agent to be included with the required freight load verification questions (Flight number; tail number; destination.). We should specifically ask the question; 'are Dangerous Goods Forms required for this flight?' After that question is answered; either yes or no; this should be a required checkmark next to the Dangerous Goods Form statement on the load sheet. This would provide the opportunity for a last-minute crosscheck on what is printed next to the Dangerous Goods Form statement and hopefully generate questions or stop something like this from happening again.'