This building is identified as the former Dickinson State Bank. Few legacy buildings from the early 20th century remain in Dickinson, and this, from the 1920's, is among them.
The First National Bank of Dickinson is not.

The First National Bank of Dickinson was chartered, number 12855, on November 13, 1925. It closed December 19, 1933.

It printed 1902 Plain Backs and 1929 Type 1's. Eight notes are in the census: four Plain Backs and four Type 1's. One Uncirculated Plain Back is in the Philpott-Moody Collection.

This Type 1, sold September, 2009, for $2,530.

[Image Heritage Auctions]

"Dickinson, TX - $5 1929 Ty. 1 The First NB Ch. # 12855
An extremely rare note from the only bank chartered in this tiny Galveston County community. This is the nicest of the four Series 1929 examples in the census, and one which traces its pedigree back to the Irish collection sale of August, 1997. No note from Dickinson has been offered since 2005, when a very well circulated and quite low end specimen realized over $1400, making it very likely that our estimate for this pleasing Fine-Very Fine example will prove quite conservative. From The Lone Star Collection"