Alexei Shvetsov and Kelsy Sannikov are suspected of concealing information about circumstances posing a danger to people's health and life.
The incident occurred at 2:30 p.m. local time (09:30 GMT) at the "Delfin" (dolphin) swimming pool, owned by Chusovoi Metals Plant. The roof collapsed over an area of about 100 sq m, leaving four women and 10 children dead.
Three commissions, including one set up by the Perm Territory Prosecutor's Office, are investigating the swimming pool tragedy.
The commission set up by the pool owner concluded that the collapse of the swimming pool roof had been caused by the giving way of a corroded metal support beam and faulty construction.
"The most important reason was the rupture of a supporting metal beam due to a high level of corrosion," Perm Territory Vice Governor Nikolai Bukhvalov said, calling the building sloppily constructed and poorly maintained.