Local Controller described a departure handled as a VFR when in fact the aircraft was IFR.

Narrative

Ground Controller verbally coordinated a BE36 as 'Runway 17L VFR to Waco'; and a VFR NAS strip was posted on my position by Ground Controller. The BE36 called me on Tower frequency ready for take off; I cleared the BE36 for take off on Runway 17L and instructed to proceed on course and after ARTS data tagged instructed the BE36 to contact Departure. It was brought to my attention the next morning that the BE36 had read a clearance of 'cleared direct Waco; five thousand' to Ground Control; though Ground issued no IFR clearance or altitude; only a VFR squawk and Departure frequency; so pilot was assuming he was IFR. I have no recommendation; Ground Control was on headset so there was no way I could hear aircraft requesting IFR clearance or reading a clearance to Ground Control; perhaps if Ground Control had frequencies on loudspeaker I may have been able to question Ground of status of aircraft as IFR or VFR or requested clarification myself from pilot prior to issuing take off clearance.