Does a townhome association have the right to tell me how many pets I can have inside my home?

that is the trouble with living in an association. one loses privacy and one must abide or leave.

Yes. In California the state law allows for one pet, although our HOA allows for two pets. Check your state laws.

YOU PROBABLY SIGED A DOCUMENT OF ASSOCIATION RULES WHEN YOU MOVED INTO YOUR TOWNHOUSE. iF YOU SIGNED THE AGREEMENT AND IT SAID YOU CAN ONLY HAVE A CERTAIN NUMBER OF PETS, THEN YES, THEY HAVE THE RGHT TO TELL YOU HOW MANY YOU CAN HAVE. ASK FOR A COPY OF THE CONTRACT YOU SIGNED WITH THE DATE YOU SIGNED IT. MAYBE THIS IS A NEW RULE AND YOU SIGNED A PAPER THAT DID NOT SAY HOW MANY PETS YOU CAN HAVE.YOU NEED THE PROOF WITH YOUR SIGNATURE

Yes, though you have the right not to live there if you don't agree with their policies.

if you own the property as real estate, then the by-laws are public record, so you're expected to know them before you even buy into the situation. so if you don't like the regulation you aren't stuck ex post facto.
check the County Register of Deeds or Clerk's office

Indeed they do. They can even exercise many other restrictions, so that you do not offend or endanger your neighbors.

They can restrict breeds, set specific weight limits, limit the numbers, and presumably even restrict the sex, if they wished.

If you don't like the by-laws, you have the option of moving.