As a deity name
Name 385 of the Gayatri Sahasranāma — Devi Bhagavata Purana, as taught by Sages
As a Hindi name
No reading on this path — this spelling has no entry in our Hindi sources, and no near neighbour is attested there either. We say so rather than invent one.
As a Sanskrit word
Meaning
holy basil (small shrub venerated by Vaiṣṇavas; commonly Tulsī), & (produced from the ocean when churned), (produced from the hair of the goddess Tulasī,.)
Scripturally attestedWhy this matches what you typed
M1 · same meaning "tulasyai" is the dative of "tulasī" — the same word in a different grammatical case.
Dictionary citations
tulasī f. holy basil (small shrub venerated by Vaiṣṇavas; commonly Tulsī), BhP.; VāyuP. & PadmaP. (produced from the ocean when churned), BrahmaP. (produced from the hair of the goddess Tulasī, ii, 19.)
tulasī [tulāṃ sādṛśyaṃ syati, so-ka gaurā˚ ṅīṣ śakaṃdhvā. Tv.] The holy basil held in veneration by the Hindus, especially by the worshippers of Viṣṇu. Comp. — patraṃ (lit.) a Tulasī leaf; (fig.) a very small gift. — vivāhaḥ the marriage of an image of Bālakṛṣṇa with the holy basil, performed on the 12th day of the bright half of Kārtika. — vṛṃdāvanaḥ -naṃ a square (pb) pedestal in which the sacred basil is planted.
Caveats
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