In The Unicode Standard, Tirhuta script implementation is discussed in  Chapter 15 South and Central Asia-IV.

The Tirhuta script (formerly called Maithili) was encoded in The Unicode Standard version 7.0. The script is now encoded in the following block:

BlocksCharacter RangeAdded in Unicode VersionUnicode chart
Tirhuta 11480..114DF 7.0  U11480.pdf

A number of proposals for its inclusion have been submitted to the Unicode Technical Committee and WG2:

2005-02-07 Issues in Representation of Indic Scripts in Unicode (Unicode Conference Presentation) — Om Vikas ( 2/05-063)

2006-06-21 Request to Allocate the Maithili Script in the Unicode Roadmap — Anshuman Pandey ( L2/06-226)

2007-05-15 Proposal to Encode North Indian Accounting Signs in Plane 1 of ISO/IEC 10646 — Anshuman Pandey ( WG2 N3312,  L2/07-139)

2007-07-31 Towards an Encoding for North Indic Number Forms in the UCS — Anshuman Pandey ( WG2 N3334,  L2/07-238)

2007-10-07 Proposal to Encode North Indic Number Forms in ISO/IEC 10646 — Anshuman Pandey ( WG2 N3367,  L2/07-354)

2007-10-14 Changes in L2/07-354 North Indic Number Forms (vs. L2/07-139) — Deborah Anderson ( L2/07-390)

2009-09-30 Towards an Encoding for the Maithili Script in ISO/IEC 10646 — Anshuman Pandey ( WG2 N2765,  L2/09-329)

2011-05-05 Proposal to Encode the Tirhuta Script in ISO/IEC 10646 — Anshuman Pandey ( WG2 N4035,  L2/11-175)

2017-04-17 Request for editorial updates to Indic scripts — Srinidhi A, Sridatta A ( L2/17-098)

Recommendations to UTC #152 July-August 2017 on Script Proposals ( L2/17-255) (See point 7.)