The City of Las Cruces reviews applications for most building projects before it issues a permit, and those applications go in through the city's Citizen Portal. Whether a blown-in attic job needs one isn't something I'll guess at. Before work starts, I check with the office that covers your address, and if a permit is needed we apply, set up the inspections and keep you posted.
Las Cruces is in climate zone 3B under New Mexico's residential energy code. Blown insulation should meet or exceed current code levels, so before you sign with anyone, us included, ask which level your attic will reach for that zone.
Here in Las Cruces and in nearby cities like Chaparral and Anthony, most of our blown-in calls are about hot bedrooms upstairs, rooms over the garage and attics that haven't been opened in years. We're based in Las Cruces, and the work is done the same way wherever the house sits.