I would not use either example to mean what you describe. I would just say, "It isn't raining now" or "It isn't raining out there."
[updated at the end to address prepositions of place and include another interpretation]
But let me paraphrase your examples to clarify a distinction between the prepositions in an on.
rain as a verb
It's raining in the streets.
Here, "the streets" (notice the plural) is another way of saying "out in the city" or "in an urban environment." This sets a mood that reminds me of detective stories and flim noir, which may not be your intent.
It's raining on the street.
The important image here is that the rainwater is hitting the pavement/roadway and getting it wet or washing something away.
rain as a noun
There's rain on the street.
This does not necessarily mean that it's currently raining, only that there is water from the sky now standing, flowing, making puddles, etc. on the pavement/roadway.
There's rain in the street.
This means almost (if not exactly) the same thing as "There's rain on the street." For "on the street" I'm more likely to imagine puddles and for "in the street" I'm more likely to imagine flowing in the gutters. Not everyone has the same imagination.
What do you mean by "the street" i.e., the wide, paved surface (object, concrete, flat/2D) or the space delimited by trees, buildings, etc. (location, abstract, space/3D)?
street as a location
It's raining in the streets.
This uses "the streets" in an abstract sense as in the phrase "Don't play in the street." It is physically impossible to play inside the flat object but it is possible to move within the space as a location. Although this example makes some sense, it is an unusual way to phrase things. I would avoid saying this except possibly in a literary or poetic work.
There's rain in the street.
This implies the location bounded by the gutters and/or curbing and water from the sky flowing through or within the space. Some people might not agree with this interpretation, so you may want to avoid this construction by rephrasing.
street as an object
It's raining on the street.
Here again, the emphasis is on the effect of the rain on a surface, getting it wet or washing something off.
There's rain on the street.
As mentioned in other answers, the word rain here would not mean falling rain but merely rainwater that has collected on the surface of the pavement/roadway.
This last interpretation is the only one where your example makes sense but its meaning is not what you intend based on your description.
"There is no rain on the street" could mean that the surface of the road is dry. Even then, since it might be wet from sources other than rainwater, it would be clearer to say, "The street is dry."