Selfadjoint Toeplitz operators with rational matrix symbols are studied using a general result concerning functions
(
T
(
z
)
−
1
x
,
y
)
(T{(z)^{ - 1}}x,y)
where
T
(
z
)
T(z)
is a polynomial family of Toeplitz operators with rational matrix symbols. It is proved that, apart from a finite number of points, these functions can be continued analytically across the boundary of the resolvent set of
T
(
z
)
T(z)
, for a dense set of
x
x
’s and
y
y
’s. This implies piecewise analyticity of the spectral measure
(
E
x
,
x
)
(Ex,x)
of selfadjoint Toeplitz operators with rational matrix symbol, for a dense set of
x
x
’s.