Service Dogs in Training unfortunately are not covered under Federal Law. Each state can set their own laws for SDIT's. California, where I live pretty much echo the Federal Law for SDIT's. Some states do not recognize SDIT's except by professional trainers and/or other restrictions.
aka, I tried to look up Nebraska Law where your profile says you reside. It does look like a SDIT friendly state though. I couldn't find wither or not documentation is required for SDIT's, but I did find this.
Nebraska State ADA Law: <---- link
Section 20-129
Denying or interfering with admittance to public facilities; penalty.
(1) Any person or agent of such person who denies or interferes with admittance to or enjoyment of the public facilities enumerated in section 20-127 or otherwise interferes with the rights of a totally or partially blind, deaf or hard of hearing, or physically disabled person under section 20-127 or sections 20-131.01 to 20-131.04 is guilty of a Class III misdemeanor.
(2) Any person or agent of such person who
denies or interferes with admittance to or enjoyment of the public facilities enumerated in section 20-127 or otherwise interferes with the rights of a bona fide trainer of a dog guide, hearing dog, or
service dog when training such dog under section 20-127 is guilty of a Class III misdemeanor.
I don't read legalizes very well, and I have a difficult time concentrating long enough to effectively read the whole section. Maybe someone else can maybe find the applicable section of law regarding asking about paperwork.