Vedic scriptures were originally in oral form only. In which period were the scriptures put in written form?
The pre-Classical form of Sanskrit is known as Vedic Sanskrit. The earliest attested Sanskrit text is the Rigveda, a Hindu scripture, from the mid-to-late second millennium BCE. No written records from such an early period survive if they ever existed. However, scholars are confident that the oral transmission of the texts is reliable: they were ceremonial literature where the exact phonetic expression and its preservation were a part of the historic tradition.
The formalization of the Sanskrit language is credited to Pāṇini, along with Patanjali's Mahabhasya and Katyayana's commentary that preceded Patanjali's work. Panini composed Aṣṭādhyāyī ("Eight-Chapter Grammar"). The century in which he lived is unclear and debated, but his work is generally accepted to be from sometime between 6th and 4th centuries BCE.
So we can safely conclude that during this period, ie., 6th and 4th centuries BCE, the Vedic Scriptures were put in the written form.
This question was dealt as early by the scholars of the Veda as early as 1889.
Also, Yaska the author of Nirukta also alludes to this issue in that codification took place when the power of oral reproduction began to decline (see Nirukata 1.20).
The scholars of the Vedas agree that in all probability the codification took place before 600 BC.
For an extensive discussion on this matter, one can refer to the works of 1. J. N. FARQTJHAR, An outline of the religious literature of India, Oxford 1920, 2. K. R. POTDAR, at Oriental Thought 3 (1957), 3. BERGAIGNE, in JA 1889 I, p. 172 ); 4. D. D. KOSAMBI, at JBBRAS 27, p. 12