We measure the dependence of the interparticle force F on the distance R between two colloidal particles with hyperbolic hedgehog defects in a nematic liquid crystal using optical tweezers. The particle-defect pair can be regarded as an elastic "dipole" in the electrostatic analogy. In a parallel configuration, where the dipole vectors are parallel with each other, F is attractive and proportional to R(-4). However, F becomes repulsive at small R due to the existence of a defect between the particles. In an antiparallel configuration, where the particles directly face each other, F is repulsive over the whole range of R and proportional to R(-3.6). In another antiparallel configuration, where two hyperbolic hedgehog defects directly face each other, F is proportional to R(-3.6) and F at small R turns out to be attractive upon tilting the dipoles. Furthermore, we yield the force between particles connected by a stringlike defect called a bubblegum defect.