I would not recommend using reclaimed rainwater from an asphalt shingle roof for any edible crop. Asphalt is petroleum-based. The runoff might be acceptable for ornamental plants, but the fact that asphalt or composite shingles tend to shed tiny particles means that those particles would be introduced to the soil around your crops.
An article from North Carolina State University Extension discusses "Water Quality of Rooftop Runoff." It doesn't specifically mention asphalt, but I don't think it would be wise to use the reclaimed water on food crops.
Green Living Journal has an article about roofing materials,and discusses asphalt shingles as well as alternatives.
The National Gardening Association site has a report that describes rainwater harvesting.
"Water from the rain barrel is, of course, not potable, but some experts also raise concern about possible contaminants from rooftops that can make the water unsuitable for edible gardens. According to an article in Landscape Architecture magazine, asphalt shingles and other porous or rough roofing materials can hold particulates such as bird droppings and other debris, as well as heavy metals from the air, which then wash into the rain barrel. Wood shingles that are chemically treated to resist rot and algae can leach the chemicals into the rainwater running off the roof. Zinc strips that prevent moss build-up can also be problematic. Some large-scale rainwater collection systems are even designed to allow for the first flush of water off the roof -- which carries the majority of the questionable substances -- to be diverted.
Other people dispute these risks and say washing your garden produce is all that's needed. It's a judgment call. I tend to research things to death so I think it would be interesting to have some of my rooftop runoff tested at the health department."
If installing slate, clay tiles, untreated wood shingles, or a green roof is prohibitively expensive, the best solution might be to landscape the garden in such a way that you can reclaim runoff from the roof for non-edible plants.