If the constrained Hamiltonian systems have a _finite_ number of _real_ degrees of freedom$^1$, and if all the constraints are regular, then it is mathematically impossible to have an _odd_ number of [second-class constraints](http://en.wikipedia.org/wiki/First_class_constraint#Second_class_constraints). (The proof is very similar to the reason why a symplectic [manifold](http://en.wikipedia.org/wiki/Symplectic_manifold) or [vector space](http://en.wikipedia.org/wiki/Symplectic_vector_space) must be even-dimensional.)

Perhaps OP is actually considering a constrained Hamiltonian field theory with an _infinite_ number of degree of freedom and an _infinite_ number of second-class constraints? (Typically this happens because all the fields, say a position field $\phi(\vec{x},t)$ and a momentum field $\pi(\vec{x},t)$, are labeled by a _continuous_ index, namely the space point $\vec{x}$). In that case, it does not make sense to label $\infty$ as an odd number.

_Example:_ A typical example of a second-class constraints in 1+1 dimension field theory with canonical equal-time Poisson brackets 
$$\tag{1} \{\phi(x,t),\pi(y,t)\}~=~ \delta(x-y), $$ 
$$\tag{2}  \{\phi(x,t),\phi(y,t)\}~=~0, $$
$$\tag{3}  \{\pi(x,t),\pi(y,t)\}~=~0, $$
is

$$\tag{4} \chi(x,t)~:=~\pi(x,t) -\partial_x\phi(x,t). $$

Naively one may think of (4) as a single (i.e. odd!) second-class constraint, but it is really infinitely many second-class constraints labeled by the position $x$. Their equal-time Poisson brackets are

$$\tag{5} \Delta(x,y)~:=~\{\chi(x,t),\chi(y,t)\}~=~ 2 \delta^{\prime}(x-y) $$

with a formal$^3$ inverse

$$\tag{6} \Delta^{-1}(x,y) ~=~ \frac{1}{4}{\rm sgn}(x-y).$$

For another related example of second-class constraints in Hamiltonian field theory, see also e.g. [this](http://physics.stackexchange.com/a/15392/2451) Phys.SE answer.

----

$^1$ The definition of [degrees of freedom](http://en.wikipedia.org/wiki/Degrees_of_freedom_%28physics_and_chemistry%29) (d.o.f.) is e.g. discussed in [this](http://physics.stackexchange.com/q/8860/2451) Phys.SE post. (Note that there is also a field-theoretic notion of d.o.f., which is different. E.g. in pure QED in 3+1 dimensions, the photon has 2 physical polarizations, so one would often say that pure QED has 2 physical d.o.f., etc. This is not the notion of d.o.f, that I'm considering here. If OP is counting field-theoretic d.o.f., there is no reason to be surprised to meet an odd number.)

$^2$ This example is sometimes referred to as chiral or self-dual bosons in 
1+1 dimensions.

$^3$ One should impose appropriate boundary conditions at $|x| \to \infty$.