There seems to be no ironclad system which associates number of hit dice with creature size, even if hit dice appear in limited ranges for given creature sizes. This may cause some trouble when designing creatures, and leaves as an open question why the designers did not use more fixed assignments and different methods for manipulating hit points (such as more varied Constitution scores).
Small and Medium-sized humanoids tend to have 1 hit die (except for kobolds, which only have 1/2). No Medium creature has less than 1, but may have much more in many cases, and so can Small ones; even Tiny creatures can have 1 full hit die (some 5 animals in the MM), or more (like pseudodragons, homuncluli, and imps with 2 or 3; meanwhile, Tiny dragons have 3-5 hit dice, or even as high as 6-7 for advanced metallics).
Let's restrict ourselves to looking at creatures with some fractional hit die in the MM:
| HD | Dim. | Tiny | Small | Med. |
|---|---|---|---|---|
| 1/4 | 2* | 4 | 0 | 0 |
| 1/2 | 0 | 8 | 3** | 0 |
* Includes the bat and toad (from animal appendix).
** Includes the kobold, small skeleton, and small monstrous centipede.
The interesting thing is that for all these creatures which have resorted to fractional hit dice, their Constitutions remain near human levels. This can be particularly suspicious when considered alongside their much lower Strength scores; consider the bat (Str 1, Con 10), toad (Str 1, Con 11), small centipede (Str 5, Con 10), and kobold (Str 6, Con 11). Other fractional-hit-dice creatures follow the same pattern.
Even more telling evidence comes from the Skip Williams article, "How to Create a Monster". This document includes tables detailing baseline statistics for all 17 different monster types, in each of the 9 different size categories; in not a single one of any of these 150+ cases is there recommended a Constitution score any less than the range of 10-11. Even Fine creatures are shown with base Hit Dice going as low as 1/8 d8 or 1/16 d8, but maintaining a full Constitution score of at least 10.
My opinion is that fractional hit dice may be justified in some circumstances, for very reduced creature sizes. However, it would be more convenient and reasonable to maintain a full hit die and reduce the Constitution score for very small creatures; it would make it easier to advance them smoothly, and would maintain the deficiency when class levels are taken. For example, kobolds as written have 1st-level Warriors who are no less durable than human or orcish 1st-level Warriors, even though the base creature has only half a hit die -- any such War1 has Con 11 for a full 1d8 hit dice and 4 hit points, on average (and this equity is true for all other classes and levels, as well). If I had been among the designers, I would have given kobolds Con 7, for hit dice of 1d8-2 (which again gives, on average, between 2 and 3 hit points); and while I'm at it, I wish that goblins had Con 9, for hit dice of 1d8-1, as in previous rulesets. (Additionally, it is clear the Dragons have wildly superior hit dice for each size category as compared to any other creature, probably unreasonably so.)
So, it's a bit of a mystery why the designers of D&D 3rd Edition decided to bar themselves from ever giving any monster less than a Constitution of 10, and instead relied on diminishingly small (and effectively indistinguishable) fractions of a hit die for very small creatures. Using the already-in-place Constitution mechanism would have allowed the same averages to be achieved (for example: 1/2 d8 = 1d8-2 [Con 6], while 1/4 d8 = 1d8-3 [Con 4], etc.), would have made for simpler hit-point rolling, and would have scaled consistently with added hit dice or character levels. Instead, on the face of it, Elves seem to be the only race in existence who by their nature have Constitution penalties. It's an odd choice to have made.