I have come up with some chase rule but they are not written down yet.
I use ref saves, combined with con checks.
I use con checks for exaustion as per the core rulebooks.
Now for the ref saves.
1) Decide on the length of time/distance that a check will cover. For short or city based chasses 1 - 10 rounds is a good rule of thumb. For longer, overland/marathon, chases 1 - 24 hours seems to work well. The basic idea is do not exceed 12 checks, it just gets boring.
2) Assign a DC for the current check. Running has a base DC of 10. Then you apply appropriate modifiers for rough ground, crowded streets, unstable surfaces, etc.
3) The armor's max dex applies to the REF bonus in this case.
4) Roll the ref and con checks.
5) If the DC is missed by less then 5 the person moved their normal movement, exceeds by less then 5 the person moved double their movement, exceeds by more then 5 the person moved tripple their movement. Roll natural 1, the person fell which can be deadly depending on the situation. Roll natural 20, the person ran quadrouple their normal rate.
6) Describe the action appropriatly. This is the key part to mooding the chase scene.