Yes. There is an exception to the warrant requirement known as hot pursuit. This means the police are chasing a suspect. They don't have to end the chase just because they go into their house.
I am a former federal and State prosecutor and now handle criminal defense and personal injury/civil rights cases. Feel free to check out my web site and contact me at (212) 385-8015 or via email at Eric@RothsteinLawNY.com. The above answer is for informational purposes only and not meant as legal advice.
If it is a chase/hot pursuit, the police officers actions may be justified/lawful.
A lot depends on the various facts involved. You need to speak w/an attorney to go all of the issues.
Joseph A. Lo Piccolo, Esq.
Hession Bekoff & Lo Piccolo, LLP
President, Criminal Courts Bar Association of Nassau County
1103 Stewart Avenue, Suite 200
Garden City, NY 11530