There is no prohibition of overlapping coverage in IPRs in the TRIPS agreement.
There is no direct mention of an overlap between patents and copyright in the TRIPS agreement. This is not surprising, since patent–copyright overlap is rather an edge case: outside of a very small subset of software patents, there is no possibility of an overlap.
However, from first principles, the TRIPS agreement mandates patent protection for "inventions, whether products or processes, in all fields of technology" (TRIPS art 27). It also mandates copyright protection for literary and artistic works, including computer programs (TRIPS art 10).
Since the TRIPS agreement does not provide any exceptions to these obligations, a member of the agreement must allow for both kinds of protection even if there would be an overlap.
Other types of intellectual property
There is evidence of allowable overlaps in other types of IPRs, notably designs and copyright.
The TRIPS agreement subtly hints, at article 25(2) at one possible overlap: that between designs and copyright of textiles.
Each Member shall ensure that requirements for securing protection for textile designs, in particular in regard to any cost, examination or publication, do not unreasonably impair the opportunity to seek and obtain such protection. Members shall be free to meet this obligation through industrial design law or through copyright law.
There is therefore the presumption that a textile could validly be protected under either.
The TRIPS agreement also implements, at art 9, the Berne Convention for the Protection of Literary and Artistic Works. The Berne Convention explicitly notes, at art 2(7), how a broader category of industrially-applied art is protected:
Subject to the provisions of Article 7(4) of this Convention, it shall be a matter for legislation in the countries of the Union to determine the extent of the application of their laws to works of applied art and industrial designs and models, as well as the conditions under which such works, designs and models shall be protected. Works protected in the country of origin solely as designs and models shall be entitled in another country of the Union only to such special protection as is granted in that country to designs and models; however, if no such special protection is granted in that country, such works shall be protected as artistic works.
This therefore acknowledges a clear overlap between copyright and designs, and explicitly leaves it to individual members to decide on how to handle it.