IIABNY members often call the Research Department with this question. Here are the rules:
In general, an excess line broker may not place a risk with a non-admitted carrier unless she has obtained three declinations from admitted carriers. These carriers must be licensed to write the kind of insurance in question. In addition, she must have reason to believe those carriers might consider writing the type of coverage or class of insurance involved. New York Insurance Regulation 41 lists five criteria on which the broker can base her reason to believe that these carriers were markets. For example, recently writing that type of coverage or class of insurance; advertising; articles in the media; and conversations with other insurance producers are all valid reasons.