MAF Controller described a conflict event when the RADAR Controller elected not to accept a hand off on an aircraft transitioning to a near by airport; but instead issued control authority to the Tower Controller.

Narrative

Just after I took the Local Control position; a C172 had just finished a practice approach to MAF and was departing VFR back to MDD and was previously coordinated as my control. A VFR point out from RADAR was a pipeline patrol and a E120 on the D-BRITE; so after the point out was given; I suggested to the RADAR Controller that he take back the C172 because he was about to leave my airspace to MDD which is just outside Towers airspace; and so he could work the C172 around his other traffic. The RADAR Controller again told me he was my control. I gave the C172 a short vector around the VFR point out; once the traffic was clear; I issued the location of the E120 which was about 8-9 north of his position westbound at around 5;000. I observed the C172 descending from 4;500 to 4;400; and also saw several targets in the vicinity of MDD. I then switched the C172 to advisories. Several minutes later the RADAR Controller called and asked me to keep the E120 at 5;000 because he had already cleared him for the Visual Approach and switched him to my frequency. As soon as the RADAR Controller was done talking to me; I reached out to the E120; his first transmission to me was that he had the Cessna in sight; I rogered him and cleared him to land on 16R. At this time the C172; who has been on advisories for a few minutes; started to climb out of 4;400 to 4;800. The C172 passed in front of the E120 who was still at 5;000. Target resolution was never lost.