It sometimes happens that an object is discovered and thought to be an asteroid and then, at some later time, discovered to show cometary activity. It can also happen that a comet and an asteroid, previously thought to be different objects, are identified through orbital analysis as the same object. There are currently only three objects which are cross-listed both as a comet and as a minor planet.
(2060) Chiron = 95P/Chiron was the first Centaur discovered (1977 UB) and it had an asteroidal appearance upon discovery (C. Kowal in 1977, IAU Circular 3129). Although proposed to be cometary in physical structure shortly after discovery, it was only in the late 1980s that cometary activity was observed, first by anomalous brightening (D. Tholen and collaborators, IAU Circular 4554) and then by directly imaging the coma (K. Meech & M. Belton, IAU Circular 4770).
(7968) Elst-Pizzaro = 133P/Elst-Pizzaro is a main-belt object that was discovered by Elst and Pizzaro in 1996 and reported by them as a comet with a persistent dust tail (IAU Circular 6456). It was then linked by B. Marsden with a previously known (but not named or numbered) asteroid, 1979 OW7 (IAU Circular 6457).
(4015) Wilson-Harrington = 107P/Wilson-Harrington is an example of the second case described above. In 1992 E. Bowell located images of the minor planet (4015) 1979 VA on plates taken in 1949 in the course of the first Palomar Sky Survey. The images had a cometary appearance, rather than the expected asteroidal appearance. B. Marsden then realised that this fuzzy object was comet Wilson-Harrington (1949 III), an object that had been reported in 1949, but that had been poorly followed and was lost. See IAU Circulars 1244, 1248, 1250, 5585, and 5586.
IAU
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IAU Division III
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IAU CSBN
Department of Astronomy
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M. F. A'Hearn
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The Real World