Don't know if this is what is envisioned for you, but our historic site,
Rancho Los Cerritos in Long Beach, CA, was put under the direction of the
library system when first purchased in 1956.  Because of this administrative
connection and because the historic home had a library space (the family's
personal library), museum staff began collecting books on CA history.  We've
since become a research library, with many rare books as well as new
materials.  We are catalogued into the library's main system and anyone using
the library's data base will find our materials.

One of the advantages being under the library:  they understood our
educational mission and were very supportive of research, archival
collections, educational programming (vs. recreational programming).  A
disadvantage:  as the library's budget was cut year after year, the museum
became a true stepchild, placed on the lowest rung of the ladder for
additional funds.  This was somewhat understandable, as the library was
protecting its book budget, but it didn't do the library any good.

I think a "marriage" of the two institutions can work as long as everyone is
clear, up front, as to how the two will be administered, where priorities
will fall, etc.; and as long as you always maintain the appropriate
professional staff for both services.

If this is helpful and you want to talk more, I'm at "[log in to unmask]"
 Ellen Calomiris, Rancho Los Cerritos Historic Site, Long Beach, CA