What If the announcement for a Tenure-Track position in a research-intensive university does not request a research statement? If a TT position is announced in  a medical-related field in a research-intensive university, and they request to apply using 1) a letter of interest and 2) a CV (No research statement is required). They say the candidate's time would be divided between research 60%, teaching 20%, and service 20%. Would you still submit a research statement or would you just include in the letter of interest more details about your current and future research (this might require making the letter little longer ~3 pages)?
Yes, a three page letter of interest would not be abnormal in these circumstances. Please keep the font size large given that the faculty on search committees have aging eyes.

My guess is that they've gotten over 200 applications for a single position in previous years and are attempting to do a first cull before asking for more details and letters. They should be commended.