Abstract The small binding energy of the hypertriton leads to predictions of the non-existence of bound hypernuclei for isotriplet three-body systems such as nnΛ. However, invariant mass spectroscopy at GSI has reported events that may be interpreted as the bound nnΛ state. The nnΛ state was sought by missing-mass spectroscopy via the (e, e′K+) reaction at Jefferson Lab’s experimental Hall A. The present experiment has higher sensitivity to the nnΛ-state investigation in terms of better precision by a factor of about three. The analysis shown in this article focuses on the derivation of the reaction cross-section for the 3H(γ*, K+)X reaction. Events that were detected in an acceptance, where a Monte Carlo simulation could reproduce the data well ($|\delta p/p| \lt 4\%$), were analyzed to minimize the systematic uncertainty. No significant structures were observed with the acceptance cuts, and the upper limits of the production cross-section of the nnΛ state were obtained to be 21 and $31 \, \rm {nb} \, \rm {sr}^{-1}$ at the $90\%$ confidence level when theoretical predictions of (−BΛ, Γ) = (0.25, 0.8) MeV and (0.55, 4.7) MeV, respectively, were assumed. The cross-section result provides valuable information for examining the existence of nnΛ.