We're given information that there are currently (present tense) puddles in the road. This states a consequence - the puddles are there because of something that happened before, which caused rain.

Looking at the options:

A) "rains" is present tense but doesn't make logical sense as a reason for the current state. 

B) "will be raining" is future tense so also doesn't fit.

C) "had to rain" is correct grammar but awkward phrasing.

D) "must rain" could imply a permanent state rather than a past occurrence. 

E) "must have been raining" uses the present perfect tense to correctly imply a past action (raining) that helps explain the current situation (puddles).

Therefore, the most logical option is E - "It must have been raining".

This fits the context best by attributing the puddles to rain that is understood to have occurred before now.