FAQ: Will T4 RNA Ligase 1 ligate double stranded DNA?

No, not significantly. Contrary to early reports T4 RNA Ligase 1 does not improve blunt end ligation significantly when used with T4 DNA Ligase 1. (1).
(1) Sugino, A. et al. (1977) J. Biol. Chem. 252, 3987-3994.