All HAWAII overprinted bills were dated 1935. They were issued for use during WWII. Please see the Related Question for more information.
All special Hawaii bills issued during WWII were part of the 1934 series. Only $1 bills were dated 1935.
All $1 notes overprinted for use in Hawaii were dated 1935.
As of 01/2015, HAWAII-overprint bills retail for $10 to $40 in circulated condition. A nice uncirculated one can sell for $135 or more. Despite the word HAWAII and a 1935 date, these bills were actually printed in Washington DC during WWII. The government was afraid that if the Japanese invaded the islands, any currency they stole could used to destabilize the US economy. The Treasury's solution was to replace standard $1, $5, $10, and $20 bills in that territory with special versions that had brown seals and HAWAII overprinted on both sides. If Hawaii had been captured its special currency could be declared worthless without affecting bills used on the mainland.
There aren't any US bills dated 1936. The special HAWAII-overprint bills issued during WWII all carry a 1935 date. Please see the question "What is the value of a 1935 A US 1 dollar bill with HAWAII on it?"
During WWII special bills were printed for use by citizens in Hawaii and by troops in North Africa. They used special seal colors - brown for Hawaii and yellow for North Africa - and had those regions' names overprinted in large letters. The intent was to make the bills easy to spot so they could be declared worthless if either region had been captured by the enemy. HAWAII bills can be moderately valuable. As of 11/2011 retail prices are $10 to $40 in average condition. A nice uncirculated one can bring $135. Note: All WWII $1 bills were dated 1935 despite being issued in the 1940s. Other denominations were dated 1934.
Please check your bill again and see the Related Question. All special "Hawaii overprint" $1 bills were dated 1935.
The U.S. only printed blue-seal silver certificate $1 bills with that date. If you have an overprinted bill with a word such as HAWAII on it, please post a new question with that information, as you have an example of anti-occupation currency made for use during WW2.
It can't be 1935, because there were no $5 bills with that date.It can't be Hawaii, because at that time all US currency was printed in Washington.And it wasn't minted, because the US Mint only makes coins. Bills are printed by the BEP.What you almost certainly have is a special bill printed for use in Hawaii during World War II. The HAWAII overprint and brown seal made the bills easy to identify and declare worthless if they had fallen into enemy hands.Please look for these questions for more information:"What is the value of a 1935 US 1 dollar bill with HAWAII on it?""What is the value of a 1934 US 5 dollar bill with HAWAII on it?"
The US never printed any bills dated 1938. Hawaii bills were printed during WWII and carried a 1935 date.
The US never printed any bills dated 1937. Hawaii bills were printed during WWII and carried a 1935 date.
These bills were printed with brown seals and HAWAII on the back for use in the islands during WWII. The special printing made it easy for them to be declared worthless if they fell into enemy hands.