(3-6-21) In school history Celina has advanced to two state boys basketball tournaments, the first was in 1936 and the second was 36 years later in 1972. Celina is 0-2 in those two appearances.
Finding information on high school sports in 1936 can be quite an adventure, the 1936 Bulldogs proved the point.
In their 1936 first round Class B game played at the OSU Gym…Celina, coached by Roger Day, lost to Jamestown Ross 31-29. Ross would lose in the next game,, a quarter-final, to Leesburg 43-25. Sandusky St. Marys would beat Leesburg in the State Final Game 25-22.

The above box score on the Ohio High School Athletic Association (OHSAA) site was the only information that was found online. In 1936 the larger schools were in Class A, while smaller size schools were in Class B.
All the names listed in the box score are old-time Celina names. The team included a future Celina football and basketball coach and high school principal, Bob Brandon. Brandon was one of the younger members of the team.
Brandon would be named the Head football and basketball coach in 1946-47, yes he did both.
1946-47 Celina Boys Basketball Team

The 1936 team did not play in the Fieldhouse, it was built in 1939, but home games were played in the gym which is located in the current Celina City Schools administration building and is now used for school plays, BOE meetings, etc. This gym was not a full-length court, but one that was similar to the Hoosier Gym, many Mercer County schools had the same type of facility.