We present mid-resolution spectroscopic observations of 63 faint (V=12-16) stars identified by Kun (1992) as Hα emission candidates in an objective prism survey of several high galactic latitude molecular clouds. Only 4 stars in our sample (6%) are bona fide T Tauri stars on the basis of their strong Li I absorption and Hα emission features. They have late M spectral types (M4-M5.5) and two of them form a visual binary with separation ~7". The new T Tauris are associated with the L 134 molecular complex, the northernmost extension of the Scorpio - Ophiuchus star forming region, which has been traditionally considered as a non-star forming region. In the other high latitude clouds surveyed by Kun (1992), we have not found any T Tauri star in our follow-up spectroscopy. Most of the observed stars (~80%) are late type dwarfs without detectable Hα emission in our spectra. Eight stars are M-dwarfs with Hα in emission, but no detectable Li I λ6708 absorption. They could be post T Tauri stars or older dMe stars; more data is necessary in order to establish their evolutionary status. Our results show that Kun (1992) was able to detect weak Hα emission lines (down to equivalent width of ~1.5A) in faint stars near the plate magnitude limit (V~16), but in many cases plate defects, absorption bands and/or overlying stars were taken as possible Hα emission. In this paper we correct Kun's previous indication that there may be numerous young stars associated to high latitude molecular clouds, and we severely constrain the presence of a population of T Tauri stars in these clouds. We note that none of our four T Tauri stars is located in an isolated translucent molecular cloud.